Question

what is the sum?
\\(\frac{3}{x^2 - 9} + \frac{5}{x + 3}\\)
\\(\bigcirc \frac{8}{x^2 + x - 8}\\)
\\(\bigcirc \frac{5x - 12}{x - 3}\\)
\\(\bigcirc \frac{-5x}{(x + 3)(x - 3)}\\)
\\(\bigcirc \frac{5x - 12}{(x + 3)(x - 3)}\\)

Explanation:

Step1: Factor the denominator

$x^2 - 9 = (x+3)(x-3)$

Step2: Find common denominator

The common denominator is $(x+3)(x-3)$. Rewrite the second fraction:
$\frac{5}{x+3} = \frac{5(x-3)}{(x+3)(x-3)}$

Step3: Combine the fractions

$\frac{3}{(x+3)(x-3)} + \frac{5(x-3)}{(x+3)(x-3)} = \frac{3 + 5(x-3)}{(x+3)(x-3)}$

Step4: Simplify the numerator

$3 + 5x - 15 = 5x - 12$

Step5: Write the final fraction

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

Answer:

$\boldsymbol{\frac{5x-12}{(x+3)(x-3)}}$ (the last option)