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How do you simplify $\frac{x}{x^{2} - 9} - \frac{x}{x^{2} + 6 x + 9}$ $x/(x^2-9) - x/(x^2+6x+9)$ ?

1 Answer

Oct 2, 2015

$\frac{6 x}{x^{3} + 3 x^{2} - 9 x - 27}$ $(6x)/(x^3+3x^2-9x-27)$

Explanation:

Factoring:
$XXX x^{2} - 9 = (x + 3) (x - 3)$ $color(white)("XXX")x^2-9 = (x+3)(x-3)$
$XXX x^{2} + 6 x + 9 = (x + 3) (x + 3)$ $color(white)("XXX")x^2+6x+9 = (x+3)(x+3)$

$\frac{x}{x^{2} - 9} - \frac{x}{x^{2} + 6 x + 9}$ $x/(x^2-9) - x/(x^2+6x+9)$

$XXX = \frac{x (x + 3) - x (x - 3)}{(x + 3) (x + 3) (x - 3)}$ $color(white)("XXX")=(x(x+3)-x(x-3))/((x+3)(x+3)(x-3))$

$XXX = \frac{6 x}{x^{3} + 3 x^{2} - 9 x - 27}$ $color(white)("XXX")=(6x)/(x^3+3x^2-9x-27)$

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