Question

What is the sum? A B C D

Answer 1

Answer:

$\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }$

Step-by-step explanation:

We are given the expression:

$\displaystyle{\dfrac{3}{x^2-9} + \dfrac{5}{x+3}}$

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

$\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5}{x+3}}$

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

$\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5(x-3)}{(x+3)(x-3)}}$

Add both together since they have same denominator now:

$\displaystyle{\dfrac{3+5(x-3)}{(x+3)(x-3)} }$

Simplify the numerator:

$\displaystyle{\dfrac{3+5x-15}{(x+3)(x-3)} }\\\\\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }$

Therefore, the sum is:

$\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }$