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

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Answer 1 · 2018-07-02T08:38:39

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

As explained below:

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

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

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

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

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

So we get:

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

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

Hence we get:

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

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

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

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

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