How do you simplify $x^2/(x^3-125)+5/(x^2+5x+25)$ ?

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Answer 1 · 2015-02-04T15:19:48

The answer is: $(x^2+5x-25)/((x-5)(x^2+5x+25))$ .

First of all, we have to factor all the denominators.

$x^3-125=x^3-5^3=(x-5)(x^2+5x+25)$ , with the polynomial $x^2+5x+25$ no more factored.

I remember that $a^3-b^3$ are called "difference of cubes", and it could be factored:

$a^3-b^3=(a+b)(a^2-ab+b^2)$ .

So:

$x^2/((x-5)(x^2+5x+25))+5/(x^2+5x+25)=$

$=(x^2+5(x-5))/((x-5)(x^2+5x+25))=(x^2+5x-25)/((x-5)(x^2+5x+25))$

How do you simplify x^2/(x^3-125)+5/(x^2+5x+25)x^2/(x^3-125)+5/(x^2+5x+25)?