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Math Problems
Algebra 2
Multiply and divide rational expressions
Divide. Write your answer in simplest form.
\newline
14
g
−
7
g
+
1
÷
3
g
+
5
3
g
\frac{14g - 7}{g + 1} \div \frac{3g + 5}{3g}
g
+
1
14
g
−
7
÷
3
g
3
g
+
5
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Divide. Write your answer in simplest form.
\newline
v
−
5
35
v
+
14
÷
v
−
5
7
\frac{v - 5}{35v + 14} \div \frac{v - 5}{7}
35
v
+
14
v
−
5
÷
7
v
−
5
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Multiply. Write your answer in simplest form.
\newline
4
k
−
3
5
k
×
(
k
2
−
1
)
\frac{4k - 3}{5k} \times (k^2 - 1)
5
k
4
k
−
3
×
(
k
2
−
1
)
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Multiply. Write your answer in simplest form.
\newline
3
p
2
−
4
p
5
p
+
4
×
5
p
+
4
p
\frac{3p^2 - 4p}{5p + 4} \times \frac{5p + 4}{p}
5
p
+
4
3
p
2
−
4
p
×
p
5
p
+
4
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Divide. Write your answer in simplest form.
\newline
m
−
4
10
m
3
−
6
m
2
÷
7
5
\frac{m - 4}{10m^3 - 6m^2} \div \frac{7}{5}
10
m
3
−
6
m
2
m
−
4
÷
5
7
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Multiply. Write your answer in simplest form.
\newline
5
u
−
4
u
2
×
(
u
−
4
)
\frac{5u - 4}{u^2} \times (u - 4)
u
2
5
u
−
4
×
(
u
−
4
)
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Multiply. Write your answer in simplest form.
\newline
6
m
5
×
(
4
m
−
5
)
\frac{6m}{5} \times (4m - 5)
5
6
m
×
(
4
m
−
5
)
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Multiply. Simplify your answer.
\newline
13
y
2
z
3
y
z
×
8
y
8
y
2
z
\frac{13y^2z}{3yz} \times \frac{8y}{8y^2z}
3
yz
13
y
2
z
×
8
y
2
z
8
y
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Multiply. Simplify your answer.
\newline
8
w
x
2
15
w
2
x
⋅
17
w
19
w
\frac{8wx^2}{15w^2x} \cdot \frac{17w}{19w}
15
w
2
x
8
w
x
2
⋅
19
w
17
w
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Multiply. Write your answer in simplest form.
\newline
3
p
3
−
p
2
5
p
+
1
×
4
p
+
5
2
\frac{3p^3 - p^2}{5p + 1} \times \frac{4p + 5}{2}
5
p
+
1
3
p
3
−
p
2
×
2
4
p
+
5
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Multiply. Write your answer in simplest form.
\newline
p
+
3
p
2
×
p
2
7
p
+
21
\frac{p + 3}{p^2} \times \frac{p^2}{7p + 21}
p
2
p
+
3
×
7
p
+
21
p
2
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Divide. Write your answer in simplest form.
\newline
21
j
−
14
j
÷
6
\frac{21j - 14}{j} \div 6
j
21
j
−
14
÷
6
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Multiply. Write your answer in simplest form.
\newline
9
c
2
−
1
c
−
1
×
(
c
−
1
)
\frac{9c^2 - 1}{c - 1} \times (c - 1)
c
−
1
9
c
2
−
1
×
(
c
−
1
)
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Divide. Write your answer in simplest form.
\newline
30
v
−
12
v
2
÷
6
v
2
\frac{30v - 12}{v^2} \div \frac{6}{v^2}
v
2
30
v
−
12
÷
v
2
6
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Multiply. Write your answer in simplest form.
\newline
4
g
2
+
g
−
5
5
g
−
3
×
5
g
−
3
4
g
+
5
\frac{4g^2 + g - 5}{5g - 3} \times \frac{5g - 3}{4g + 5}
5
g
−
3
4
g
2
+
g
−
5
×
4
g
+
5
5
g
−
3
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Multiply. Simplify your answer.
\newline
3
v
20
v
2
w
2
×
18
v
w
\frac{3v}{20v^2w^2} \times 18vw
20
v
2
w
2
3
v
×
18
v
w
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Multiply. Write your answer in simplest form.
\newline
40
n
−
16
2
n
+
5
×
2
n
+
5
8
\frac{40n - 16}{2n + 5} \times \frac{2n + 5}{8}
2
n
+
5
40
n
−
16
×
8
2
n
+
5
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Multiply. Write your answer in simplest form.
\newline
s
−
3
3
s
−
1
×
3
s
−
1
s
2
−
3
s
\frac{s - 3}{3s - 1} \times \frac{3s - 1}{s^2 - 3s}
3
s
−
1
s
−
3
×
s
2
−
3
s
3
s
−
1
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Multiply. Write your answer in simplest form.
\newline
v
2
−
4
4
v
−
5
×
(
4
v
−
5
)
\frac{v^2 - 4}{4v - 5} \times (4v - 5)
4
v
−
5
v
2
−
4
×
(
4
v
−
5
)
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Divide. Write your answer in simplest form.
\newline
v
−
5
5
v
−
1
÷
(
5
v
2
−
26
v
+
5
)
\frac{v - 5}{5v - 1} \div (5v^2 - 26v + 5)
5
v
−
1
v
−
5
÷
(
5
v
2
−
26
v
+
5
)
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Divide. Write your answer in simplest form.
\newline
k
2
−
9
3
k
÷
8
7
\frac{k^2 - 9}{3k} \div \frac{8}{7}
3
k
k
2
−
9
÷
7
8
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Divide. Simplify your answer.
\newline
20
d
9
c
2
÷
16
c
d
2
19
c
d
2
\frac{20d}{9c^2} \div \frac{16cd^2}{19cd^2}
9
c
2
20
d
÷
19
c
d
2
16
c
d
2
\newline
______
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Divide. Write your answer in simplest form.
\newline
8
s
9
s
2
−
15
s
+
4
÷
3
5
s
+
2
\frac{8s}{9s^2 - 15s + 4} \div \frac{3}{5s + 2}
9
s
2
−
15
s
+
4
8
s
÷
5
s
+
2
3
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Multiply. Write your answer in simplest form.
\newline
2
q
+
3
q
2
×
(
10
q
2
−
13
q
+
4
)
\frac{2q + 3}{q^2} \times (10q^2 - 13q + 4)
q
2
2
q
+
3
×
(
10
q
2
−
13
q
+
4
)
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Multiply. Write your answer in simplest form.
\newline
2
q
+
1
q
2
×
9
q
2
−
6
q
+
1
3
q
+
2
\frac{2q + 1}{q^2} \times \frac{9q^2 - 6q + 1}{3q + 2}
q
2
2
q
+
1
×
3
q
+
2
9
q
2
−
6
q
+
1
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Multiply. Write your answer in simplest form.
\newline
2
y
−
3
3
y
+
5
×
5
y
−
4
y
−
4
\frac{2y - 3}{3y + 5} \times \frac{5y - 4}{y - 4}
3
y
+
5
2
y
−
3
×
y
−
4
5
y
−
4
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Divide. Write your answer in simplest form.
\newline
25
d
+
20
7
d
2
÷
3
d
−
1
3
d
+
2
\frac{25d + 20}{7d^2} \div \frac{3d - 1}{3d + 2}
7
d
2
25
d
+
20
÷
3
d
+
2
3
d
−
1
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Multiply. Write your answer in simplest form.
\newline
4
q
−
5
20
q
2
−
21
q
−
5
×
(
5
q
+
1
)
\frac{4q - 5}{20q^2 - 21q - 5} \times (5q + 1)
20
q
2
−
21
q
−
5
4
q
−
5
×
(
5
q
+
1
)
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Divide. Write your answer in simplest form.
\newline
3
12
u
3
+
20
u
2
3
\frac{3}{12}u^{3} + \frac{20u^{2}}{3}
12
3
u
3
+
3
20
u
2
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Multiply. Write your answer in simplest form.
\newline
n
−
4
5
n
×
3
n
2
+
11
n
−
4
n
−
4
\frac{n - 4}{5n} \times \frac{3n^2 + 11n - 4}{n - 4}
5
n
n
−
4
×
n
−
4
3
n
2
+
11
n
−
4
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Multiply. Write your answer in simplest form.
\newline
3
q
+
5
3
q
−
5
×
(
2
q
+
3
)
\frac{3q + 5}{3q - 5} \times (2q + 3)
3
q
−
5
3
q
+
5
×
(
2
q
+
3
)
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Divide. Write your answer in simplest form.
\newline
3
n
+
1
n
−
1
÷
2
\frac{3n + 1}{n - 1} \div 2
n
−
1
3
n
+
1
÷
2
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Divide. Simplify your answer.
\newline
5
q
13
q
2
r
÷
13
q
r
\frac{5q}{13q^2r} \div 13qr
13
q
2
r
5
q
÷
13
q
r
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Multiply.
\newline
x
2
+
4
x
+
3
x
−
1
⋅
x
+
2
4
x
+
12
\frac{x^{2}+4 x+3}{x-1} \cdot \frac{x+2}{4 x+12}
x
−
1
x
2
+
4
x
+
3
⋅
4
x
+
12
x
+
2
\newline
Simplify your answer as much as possible.
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(a)
−
3
7
\frac{-3}{7}
7
−
3
with denominator
49
49
49
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Fill in the blanks with numerals.
\newline
\newline
14
□
=
□
14 \square = \square
14
□
=
□
+
40
+
7
+40+7
+
40
+
7
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Select all the expressions that are equivalent to
6
−
9
×
6
2
6^{-9} \times 6^2
6
−
9
×
6
2
.
\newline
Multi-select Choices:
\newline
(A)
6
−
7
6^{-7}
6
−
7
\newline
(B)
1
6
7
\frac{1}{6^7}
6
7
1
\newline
(C)
6
−
18
6^{-18}
6
−
18
\newline
(D)
1
6
−
7
\frac{1}{6^{-7}}
6
−
7
1
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If
d
y
d
x
=
2
−
y
\frac{d y}{d x}=2-y
d
x
d
y
=
2
−
y
, and if
y
=
1
y=1
y
=
1
when
x
=
1
x=1
x
=
1
, then
y
=
y=
y
=
\newline
(A)
2
−
e
x
−
1
2-e^{x-1}
2
−
e
x
−
1
\newline
(B)
2
−
e
1
−
x
2-e^{1-x}
2
−
e
1
−
x
\newline
(C)
2
−
e
−
x
2-e^{-x}
2
−
e
−
x
\newline
(D)
2
+
e
−
x
2+e^{-x}
2
+
e
−
x
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Evaluate. Show your work.
\newline
0.0036
×
20
0.0036 \times 20
0.0036
×
20
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Factor completely.
\newline
20
f
3
−
10
f
2
+
2
f
−
1
20 f^{3}-10 f^{2}+2 f-1
20
f
3
−
10
f
2
+
2
f
−
1
Get tutor help
Rewrite in simplest terms:
8
(
0.6
x
−
0.1
)
+
2
(
0.9
x
−
0.6
)
8(0.6 x-0.1)+2(0.9 x-0.6)
8
(
0.6
x
−
0.1
)
+
2
(
0.9
x
−
0.6
)
\newline
Answer:
Get tutor help
Rewrite in simplest terms:
−
2
(
0.9
m
+
0.4
n
)
+
7
n
−
8
(
−
0.4
n
−
0.6
m
)
-2(0.9 m+0.4 n)+7 n-8(-0.4 n-0.6 m)
−
2
(
0.9
m
+
0.4
n
)
+
7
n
−
8
(
−
0.4
n
−
0.6
m
)
\newline
Answer:
Get tutor help
Rewrite in simplest terms:
−
8
(
0.7
q
+
0.5
r
)
−
4
r
−
2
(
0.4
r
−
0.9
q
)
-8(0.7 q+0.5 r)-4 r-2(0.4 r-0.9 q)
−
8
(
0.7
q
+
0.5
r
)
−
4
r
−
2
(
0.4
r
−
0.9
q
)
\newline
Answer:
Get tutor help
Question
\newline
For
j
(
x
)
=
(
4
x
2
−
8
)
(
−
5
x
2
−
8
x
)
j(x)=\left(4 x^{2}-8\right)\left(-5 x^{2}-8 x\right)
j
(
x
)
=
(
4
x
2
−
8
)
(
−
5
x
2
−
8
x
)
, find
j
′
(
x
)
j^{\prime}(x)
j
′
(
x
)
by applying the product rule.
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Simplify:
\newline
(
7
t
y
)
×
(
3
t
)
(7ty) \times (3t)
(
7
t
y
)
×
(
3
t
)
\newline
A.
10
t
y
10 ty
10
t
y
\newline
B.
21
t
y
21 ty
21
t
y
\newline
C.
10
t
2
y
10t^{2}y
10
t
2
y
\newline
D.
21
t
2
y
21t^{2}y
21
t
2
y
Get tutor help
Combine like terms.
\newline
−
1
+
x
−
x
3
−
x
+
3
x
3
−
1
+
5
x
3
-1+x-x^{3}-x+3 x^{3}-1+5 x^{3}
−
1
+
x
−
x
3
−
x
+
3
x
3
−
1
+
5
x
3
\newline
Answer:
Get tutor help
Combine like terms.
\newline
3
−
5
y
−
7
x
3
−
2
−
1
+
4
x
3
−
y
3-5 y-7 x^{3}-2-1+4 x^{3}-y
3
−
5
y
−
7
x
3
−
2
−
1
+
4
x
3
−
y
\newline
Answer:
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Combine like terms.
\newline
6
y
3
−
7
−
1
−
x
−
4
y
3
−
4
x
+
2
y
3
6 y^{3}-7-1-x-4 y^{3}-4 x+2 y^{3}
6
y
3
−
7
−
1
−
x
−
4
y
3
−
4
x
+
2
y
3
\newline
Answer:
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Combine like terms.
\newline
5
x
2
+
5
x
2
−
7
y
+
3
+
5
−
7
−
6
x
2
5 x^{2}+5 x^{2}-7 y+3+5-7-6 x^{2}
5
x
2
+
5
x
2
−
7
y
+
3
+
5
−
7
−
6
x
2
\newline
Answer:
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Combine like terms.
\newline
4
x
+
5
y
3
−
5
x
3
−
4
y
3
+
5
x
+
x
+
4
y
3
4 x+5 y^{3}-5 x^{3}-4 y^{3}+5 x+x+4 y^{3}
4
x
+
5
y
3
−
5
x
3
−
4
y
3
+
5
x
+
x
+
4
y
3
\newline
Answer:
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