Question

What is the simplified form of x plus 4 over x squared minus 3x minus 10 ⋅ x minus 3 over x squared plus x minus 12 ?

Answer 1

Answer: 2x^3 - x^2 - 12x - 18

Explanation:

Cross multiply, so you get

(x+4)×(x^2+x-12) = x^3 + x^2 - 12x + 4x^2 + 4x - 48

(x-3)×(x^2+x-12) = x^3 - 3x^2 - 10x - 3x^2 + 6x + 30

Add like terms together

x^3 + x^3 = 2x^3

x^2 - 3x^2 +4x^2 - 3x^2 = -x^2

-12x - 10x +4x +6x + -12x

30 - 48 = -18

So you get the big equation:

2x^3 - x^2 - 12x - 18