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Let’s check out your problem:
Evaluate:
\newline
∑
n
=
2
4
(
n
x
+
2
)
\sum_{n=2}^{4}(n x+2)
n
=
2
∑
4
(
n
x
+
2
)
\newline
Answer:
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Home
Math Problems
Algebra 2
Evaluate rational expressions II
Full solution
Q.
Evaluate:
\newline
∑
n
=
2
4
(
n
x
+
2
)
\sum_{n=2}^{4}(n x+2)
n
=
2
∑
4
(
n
x
+
2
)
\newline
Answer:
Evaluate
n
=
2
n=2
n
=
2
:
Let's start by evaluating the expression for
n
=
2
n=2
n
=
2
. Substitute
n
=
2
n=2
n
=
2
into the expression
(
n
x
+
2
)
(nx+2)
(
n
x
+
2
)
to get
(
2
x
+
2
)
(2x+2)
(
2
x
+
2
)
.
Evaluate
n
=
3
n=3
n
=
3
:
Now, evaluate the expression for
n
=
3
n=3
n
=
3
. Substitute
n
=
3
n=3
n
=
3
into the expression
(
n
x
+
2
)
(nx+2)
(
n
x
+
2
)
to get
(
3
x
+
2
)
(3x+2)
(
3
x
+
2
)
.
Evaluate
n
=
4
n=4
n
=
4
:
Next, evaluate the expression for
n
=
4
n=4
n
=
4
. Substitute
n
=
4
n=4
n
=
4
into the expression
(
n
x
+
2
)
(nx+2)
(
n
x
+
2
)
to get
(
4
x
+
2
)
(4x+2)
(
4
x
+
2
)
.
Add Results:
Now, we will add the results from
n
=
2
n=2
n
=
2
,
n
=
3
n=3
n
=
3
, and
n
=
4
n=4
n
=
4
. Add
(
2
x
+
2
)
(2x+2)
(
2
x
+
2
)
,
(
3
x
+
2
)
(3x+2)
(
3
x
+
2
)
, and
(
4
x
+
2
)
(4x+2)
(
4
x
+
2
)
together.
(
2
x
+
2
)
+
(
3
x
+
2
)
+
(
4
x
+
2
)
=
2
x
+
3
x
+
4
x
+
2
+
2
+
2
(2x+2) + (3x+2) + (4x+2) = 2x + 3x + 4x + 2 + 2 + 2
(
2
x
+
2
)
+
(
3
x
+
2
)
+
(
4
x
+
2
)
=
2
x
+
3
x
+
4
x
+
2
+
2
+
2
Combine Like Terms:
Combine like terms to simplify the expression.
\newline
2
x
+
3
x
+
4
x
=
9
x
2x + 3x + 4x = 9x
2
x
+
3
x
+
4
x
=
9
x
and
2
+
2
+
2
=
6
2 + 2 + 2 = 6
2
+
2
+
2
=
6
, so the simplified expression is
9
x
+
6
9x + 6
9
x
+
6
.
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t
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.
\newline
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\newline
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\newline
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h
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h
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−
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=
h
−
3
−
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\newline
There may be
1
1
1
or
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solutions.
\newline
h
=
h =
h
=
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Question
What is the equation of the vertical asymptote of
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Question
What is the excluded value for
y
=
1
x
−
9
−
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y = \frac{1}{x - 9} - 9
y
=
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−
9
1
−
9
?
\newline
______
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Question
Simplify. Write your answer using whole numbers and variables.
\newline
9
k
+
4
9
k
2
+
4
k
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9
k
2
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4
k
9
k
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\newline
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Question
Divide. Write your answer in simplest form.
\newline
g
−
1
10
g
3
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25
g
2
÷
(
g
−
1
)
\frac{g- 1}{10g^3 + 25g^2} \div (g- 1)
10
g
3
+
25
g
2
g
−
1
÷
(
g
−
1
)
\newline
______
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Question
Simplify. Express your answer as a single fraction in simplest form.
\newline
5
−
3
t
3
1
\frac{5 - \frac{3}{t^3}}{1}
1
5
−
t
3
3
\newline
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