How can you evaluate #(x)/(x^2-4) - (2)/(x^2-4)#?

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Answer 1 · 2015-07-22T15:53:53

#=color(blue)(1/(x+2)#

with exclusion #x != 2#

#(x)/(x^2-4) - (2)/(x^2-4) #

Here the denominators are the same, so combining the numerators we get:

#(x- 2)/(x^2-4) #

As per property:
#color(blue)(a^2-b^2) = (a+b)(a-b)#

Similarly :
#color(blue)((x^2-4)) =(x+2)(x-2) #

Expressing the denominator in the this way, the expression becomes:

#cancel(x- 2)/color(blue)((x+2)cancel((x-2)) #

#=color(blue)(1/(x+2)#

with exclusion #x != 2#