Question

Express

2x^2+3x/(2x+3)(x-2) - 6/x^2-x-2

As a single fraction in its simplest form.

Answer 1

(x + 3)/(x + 1) .

Explanation:

2x^2 + 3x/(2x + 3)(x - 2) - 6 /x^2 - x - 2

= 2x^2 + 3x/(2x + 3)(x - 2) - 6 / (x - 2)(x + 1)

The LCM is (2x + 3)(x - 2)(x + 1) so we have

(2x^2 + 3x)(x + 1) - 6(2x + 3) x( 2x + 3)(x + 1) - 6(2x + 3)

--------------------------------------- = ------------------------------------

(2x + 3)(x - 2)(x + 1) (2x + 3)(x - 2)(x + 1)

(2x + 3)(x(x + 1) - 6) (2x + 3)(x - 2)(x + 3)

= ---------------------------- = --------------------------- = (x + 3)/(x + 1)

(2x + 3)(x - 2)(x + 1) (2x + 3)(x - 2)(x + 1)