Question

How do you simplify `(2x)/(x^2+8x+15)-(x+3)/(x+5)`?

Answer 1

`frac(x^2+8x+9)(x^2+8x+15)`

Explanation:

To simplify this one must first find the common denominator. This is found by first factoring `x^2+8x+15`.
This factors into `(x+5)(x+3)`

Next multiply the 2nd fraction by `(x+3)/(x+3)` to make the denominators equal.

`frac(2x)(x^2+8x+15)-frac(x+3)(x+5)*frac(x+3)(x+3)`

`frac(2x)(x^2+8x+15)-[(x+3)(x+3)]/[(x+3)(x+5)]`

`(x+3)(x+3)=x^2+6x+9`, so combining these,

`frac(2x)(x^2+8x+15)-frac(x^2+6x+9)(x^2+8x+15)=frac(x^2+8x+9)(x^2+8x+15)`