Question

What is the difference?

Answer 1

Answer:

$\frac{x^2+3x -12}{(x-5) (x +3)(x+7)}$

Step-by-step explanation:

Given

$\frac{x}{x^2-2x-15} - \frac{4}{x^2+2x-35}$

Required

Calculate the difference

We start by factorizing the denominator of both fractions

$\frac{x}{x^2-2x-15} - \frac{4}{x^2+2x-35}$

$\frac{x}{x^2+3x - 5x -15} - \frac{4}{x^2+7x - 5x-35}$

$\frac{x}{x(x+3) - 5(x +3)} - \frac{4}{x(x+7) - 5(x+7)}$

$\frac{x}{(x-5) (x +3)} - \frac{4}{(x-5)(x+7)}$

Take LCM

$\frac{x(x+7) - 4(x +3)}{(x-5) (x +3)(x+7)}$

Open Brackets

$\frac{x^2+7x - 4x -12}{(x-5) (x +3)(x+7)}$

$\frac{x^2+3x -12}{(x-5) (x +3)(x+7)}$

This can't be simplified any further;