Question

What is the sum?
A
B
C
D

Answer 1

`\displaystyle{(5x-12)/((x+3)(x-3)) }`

Explanation:

We are given the expression:

`\displaystyle{(3)/(x^2-9) + (5)/(x+3)}`

First, factor the denominator
`\displaystyle{x^2-9}` to
`\displaystyle{(x+3)(x-3)}` via difference of two squares:

`\displaystyle{(3)/((x+3)(x-3)) + (5)/(x+3)}`

Next, multiply the expression 5/(x+3) by
`\displaystyle{x-3}` both denominator and numerator:

`\displaystyle{(3)/((x+3)(x-3)) + (5(x-3))/((x+3)(x-3))}`

Add both together since they have same denominator now:

`\displaystyle{(3+5(x-3))/((x+3)(x-3)) }`

Simplify the numerator:

`\displaystyle{(3+5x-15)/((x+3)(x-3)) }\\\\\displaystyle{(5x-12)/((x+3)(x-3)) }`

Therefore, the sum is:

`\displaystyle{(5x-12)/((x+3)(x-3)) }`