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Simplify rational expressions

Which of the following is equivalent to

\frac{\frac{1}{y} + \frac{1}{x}}{\frac{3}{xy}}

\frac{3}{x^{2}-x-20}+\frac{1}{x^{2}+9 x+20}

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Which expression is equivalent to the sum for all

x>5

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\frac{4}{2 x^{2}+8 x}

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\frac{4 x+10}{\left(x^{2}-25\right)(x+4)}

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\frac{4 x+10}{(x-5)^{2}(x+4)}

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\frac{4 x+8}{\left(x^{2}-16\right)(x+5)}

8\sqrt{p}-2\sqrt{3}=\sqrt{3}+3\sqrt{p}

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p

is the solution to the given equation?

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1

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(3\sqrt{3})/(5)

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(9)/(5)

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(9)/(25)

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(27)/(25)

Which expression is equivalent to

9b + 5b

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13b

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14b

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b^{14}

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b + 14

Which expression is equivalent to

7j + 6j

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j^{13}

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14j

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13j

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j + 13

Which expression is equivalent to

5s + 4s

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s^9

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10s

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s + 9

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9s

Which expression is equivalent to

6h + 2h

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7h

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h + 8

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8h

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h^8

Which expression is equivalent to

5u + 6u

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11u

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12u

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u^{11}

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u + 11

Which expression is equivalent to

7m + 6m

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13m

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m^{13}

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m + 13

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12m

Which expression is equivalent to

6w + 8w

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14w

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13w

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w + 14

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w^{14}

Which expression is equivalent to

9p + 9p

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19p

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p^{18}

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p + 18

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18p

Which expression is equivalent to

2k + 3k

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k + 5

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5k

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4k

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k^5

Select the expressions that are equivalent to

8m + 8m

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Multi-select Choices:

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12m - m + 5m

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16m

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15m

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12m + 5m

Select the expressions that are equivalent to

7z + 2z

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Multi-select Choices:

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9z

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z \times 9

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3z + 6z

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3z + 4z + 2z

Select the expressions that are equivalent to

4q + 9q

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Multi-select Choices:

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3q + q + 9q

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10q + 3q

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13q

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q^{13}

Select the expressions that are equivalent to

7h + 2h

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Multi-select Choices:

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4h + 6h

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9h

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h^9

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8h

Select the expressions that are equivalent to

9f + 6f

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Multi-select Choices:

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16f

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f \times 15

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f^{15}

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f + 15

Select the expressions that are equivalent to

2a + 2a

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Multi-select Choices:

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a \times 4

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4a

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a + 4

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3a + 2a

Select the expressions that are equivalent to

7h + 4h

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Multi-select Choices:

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11h

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2h + 9h

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h^{11}

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h \times 11

Which of the following is an integer?

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0

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\frac{5}{8}

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\frac{1}{3}

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\frac{2}{6}

Each table in the banquet hall has

c

chairs. There are

15

tables in the banquet hall. Choose the expression that shows the total number of chairs.

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15 + c

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\frac{15}{c}

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15c

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15 - c

3c-5=d

, which of the following correctly gives

c

d

1

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c=\frac{d-5}{3}

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c=\frac{d+5}{3}

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c=3d-5

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c=3d+15

Chere are many ways in which the list

0,1,2,3,4,5,6,7,8,9

can be separated into groups. For example, this list could be separated into the four groups

0,3,4,8

1,2,7

6

5,9

. The sum of the numbers in each of these four groups is

15,10,6,

14

, respectively. In how many ways can the list

0,1,2,3,4,5,6,7,8,9

e separated into at least two groups so that the sum of the numbers in each group the same?

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26

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29

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0,3,4,8

0

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0,3,4,8

1

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0,3,4,8

2

Which of the following is a whole number?

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\frac{5}{3}

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\frac{4}{5}

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0

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-8

Which of the following is a whole number?

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\frac{4}{9}

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0

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-7

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-9

Which of these are equal to

-7

? Select all that apply.

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Multi-select Choices:

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\frac{49}{-7}

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\frac{49}{7}

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-\frac{49}{7}

Which of these are equal to

12

? Select all that apply.

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Multi-select Choices:

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\frac{72}{-6}

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\frac{-72}{6}

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\frac{72}{6}

Which of these are equal to

3

? Select all that apply.

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Multi-select Choices:

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-\frac{36}{12}

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\frac{36}{12}

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\frac{36}{-12}

3x-

\frac{3840}{x}

24

Rationalise the denomitor

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\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{5}}

Select the expressions that are equivalent to

6b + 5b

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Multi-select Choices:

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b^{11}

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b + 11

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11b

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9b + b

Select the expressions that are equivalent to

5q + 2q

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Multi-select Choices:

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q + 4q + 2q

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q^7

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q \times 7

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6q

Select the expressions that are equivalent to

3(6x)

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Multi-select Choices:

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(3x)6

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18x

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3 + 6x

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3(x + 5x)

Select the expressions that are equivalent to

2(9m)

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Multi-select Choices:

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9(2m)

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2 + 9m

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9m + 2

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18m

Which expression is equivalent to

3r + 2r

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5r

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r^5

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4r

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r + 5

Select the expressions that are equivalent to

4j + 8j

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Multi-select Choices:

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2j + 2j + 8j

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j + 12

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j \times 12

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13j

Select the expressions that are equivalent to

3f + 6f

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Multi-select Choices:

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9f + f

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9f

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8f

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4f + 6f

Select all the numbers that are irrational.

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Multi-select Choices:

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\sqrt{2}

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\frac{2}{3}

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0.\overline{8}

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\frac{\pi}{2}

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-4.99

Expand each of the following, using suitable identities:

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(x+2 y+4 z)^{2}

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(2 x-y+z)^{2}

Which expression is equivalent to

3b + 6b

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b + 9

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8b

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b^9

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9b

Which expression is equivalent to

3h + 2h

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5h

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h^5

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4h

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h + 5

Select the expressions that are equivalent to

2q + q

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Multi-select Choices:

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2q

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4q - q

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q + q + q

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3q

Select the expressions that are equivalent to

6(u + 5)

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Multi-select Choices:

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(u \cdot 5)6

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30u + 6

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6u + 30

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30u

Select the expressions that are equivalent to

3(m + 9)

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Multi-select Choices:

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(m + 9)3

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27m

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27m + 3

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12m

Select the expressions that are equivalent to

9k + 2k

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Multi-select Choices:

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11k

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10k + 2k

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8k + 2k

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5k + 7k

Select the expressions that are equivalent to

9(t + 4)

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Multi-select Choices:

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9(4 + t)

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13t

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(t + 4)9

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(4 + t)9

Select the expressions that are equivalent to

7(q + 4)

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Multi-select Choices:

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(4q)7

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11q

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(q + 4)7

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4(q + 7)

Write a factor that you can use to rationalize the denominator of

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\frac{\sqrt{2}}{\sqrt{5}-8}

Which equation has both

3

-3

as possible values of

x

? Select all that apply.

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Multi-select Choices:

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x^2 = 6

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x^3 = 6

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x^2 = 9

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x^3 = 9

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x^2 = 27

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x^3 = 27

Select all the expressions that are equivalent to

11^5/11^5

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Multi-select Choices:

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11^0

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11

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1

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11^{10}