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

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Answer 1 · 2017-07-06T03:17:55

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

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,

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

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