Question

What is the difference?

х
4
XP-2x-15 x2 + 2x-35
x2 + 3x+12
(x-3)(x-5)(x+7)
x(x+3-12)
(x+3)(x-5)(x+7)
x2+3x+12
(x+3)(x-5)(x+7)
x² + 3x-12
(x+3)(x-5)(x+7)

Answer 1

`(x^2+3x -12)/((x-5) (x +3)(x+7))`

Explanation:

Given

`(x)/(x^2-2x-15) - (4)/(x^2+2x-35)`

Required

Calculate the difference

We start by factorizing the denominator of both fractions

`(x)/(x^2-2x-15) - (4)/(x^2+2x-35)`

`(x)/(x^2+3x - 5x -15) - (4)/(x^2+7x - 5x-35)`

`(x)/(x(x+3) - 5(x +3)) - (4)/(x(x+7) - 5(x+7))`

`(x)/((x-5) (x +3)) - (4)/((x-5)(x+7))`

Take LCM

`(x(x+7) - 4(x +3))/((x-5) (x +3)(x+7))`

Open Brackets

`(x^2+7x - 4x -12)/((x-5) (x +3)(x+7))`

`(x^2+3x -12)/((x-5) (x +3)(x+7))`

This can't be simplified any further;