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)#