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What is the sum?

3/x^2-9 + 5/x+3
A) 8/x^2+x-6
B) 5x-12/x-3
C)-5x/(x+3(x-3)
D) 5x-12/x+3(x-3)

2 Answers

4 votes

Answer:

Sum
\Rightarrow (5x-12)/((x+3)(x-3))

D is correct

Explanation:

Given:
(3)/(x^2-9)+(5)/(x+3)

We are given a rational expression and to add the expression.

First we make common denominator and then we add them

Multiply and divide the second fraction by x-3


\Rightarrow (3)/(x^2-9)+(5(x-3))/((x-3)(x+3))


\Rightarrow (3)/(x^2-9)+(5x-15)/(x^2-9)

Now we have common denominator and write as common


\Rightarrow (3+5x-15)/(x^2-9)


\Rightarrow (5x-12)/(x^2-9)

Factor the denominator:
a^2-b^2=(a-b)(a+b)


\Rightarrow (5x-12)/((x+3)(x-3))

Hence, The sum is
\Rightarrow (5x-12)/((x+3)(x-3))

User Heine Frade
by
7.9k points
5 votes
We will use the formula a^2-b^2=(a-b)(a+b) to get the fractions to the same dominator.

3/[(x-3)(x+3)]+5/(x+3) =
3/[(x-3)(x+3)]+5(x-3)/(x+3)[(x-3)(x+3)] =
(3+5x-15)/[(x-3)(x+3)] =
(5x-12)/[(x-3)(x+3)]

The final answer is D.
User Desert Rose
by
8.4k points

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