Question

2/x-3 + x-5/9-x^2 - 3x-5/9+6x+x^2

I understand how to factor to get the denominator but the numerator when I foil and add I keep getting wrong.

Answer 1

I'm taking a wild guess on what the first expression is:


`\frac2{x-3}+(x-5)/(9-x^2)-(3x-5)/(9+6x+x^2)`

First, some factoring in the denominators:


`\frac2{x-3}+(x-5)/((3-x)(3+x))-(3x-5)/((3+x)^2)`

`\frac2{x-3}-(x-5)/((x-3)(x+3))-(3x-5)/((x+3)^2)`

Find the common denominator:


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

Combine the numerators:


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

Expand the numerator:


`((2x^2+12x+18)-(x^2-2x-15)-(3x^2-14x+15))/((x-3)(x+3)^2)`

Combine like terms:


`(-2x^2+28x+18)/((x-3)(x+3)^2)`