How do you add and simplify $\frac{x + 4}{x^{2} - 4}$ $(x+4)/(x^2-4)$ $+ \frac{- 2 x - 2}{x^{2} - 4}$ $+ (-2x-2)/(x^2-4)$ ?

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Answer 1 · 2018-07-02T08:38:39

$\frac{- 1}{x + 2}$ $(-1)/(x+2)$

As explained below:

$\frac{x + 4}{x^{2} - 4} + \frac{- 2 x - 2}{x^{2} - 4}$ $(x+4)/(x^2-4) + (-2x-2)/(x^2-4)$

$\frac{(x + 4) + (- 2 x - 2)}{x^{2} - 4}$ $((x+4) + (-2x-2))/(x^2-4)$

$\frac{x + 4 - 2 x - 2}{x^{2} - 4}$ $(x+4 -2x-2)/(x^2-4)$

$\frac{- x + 2}{x^{2} - 4}$ $(-x+2)/(x^2-4)$

Now, $x^{2} - 4$ $x^2-4$ = $(x + 2) (x - 2)$ $(x+2)(x-2)$

So we get:

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

Also, $(- x + 2)$ $(-x+2)$ = $- 1 (x - 2)$ $-1(x-2)$

Hence we get:

$\frac{- 1 (x - 2)}{(x + 2) (x - 2)}$ $(-1(x-2))/((x+2)(x-2))$

$(-1cancel(x-2))/((x+2)cancel(x-2))$

$(-1)/(x+2)$

$(x+4)/(x^2-4) + (-2x-2)/(x^2-4)$ = $(-1)/(x+2)$

How do you add and simplify (x+4)/(x^2-4)x+4x2−4(x+4)/(x^2-4) + (-2x-2)/(x^2-4)+−2x−2x2−4+ (-2x-2)/(x^2-4)?