Question

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)

Answer 1

`(3)/(x^2-9)+ (5)/(x+3)= (3)/((x+3)(x-3))+ (5)/(x+3)= (3+5(x-3))/((x+3)(x-3))=(3+5x-15)/((x+3)(x-3))=(5x-12)/((x+3)(x-3))`

Answer: D.

Answer 2

Answer:- D.
`(5x-12)/((x+3)(x-3))`

Explanation:-

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

Using identity
`a^2-b^2=(a+b)(a-b)`, we get

`=(3)/((x+3)(x-3))+(5)/(x+3)`

Taking L.C.M. of the denominator, we get

`(3+5(x-3))/((x+3)(x-3))=(3+5x-15)/((x+3)(x-3))`

`=(5x-12)/((x+3)(x-3))`

`\Rightarrow(3)/(x^2-9)+(5)/(x+3)=(5x-12)/((x+3)(x-3))`

Thus, D is the right option.