Simplify the rational expression. State any restrictions on the variable? Please check my answer/correct it

#6/((x^2-16)#-#2/((x^2-x-12)#

My Answer: #4/((x+4)(x+3)#
restrictions: x=-4,4,-3

1 Answer
MAXIMILIAN C.
Apr 13, 2018

Restrictions look good, might have been oversimplified.

Explanation:

#(6/(x^2-16))-(2/(x^2-x-12))#
Factoring bottom parts:
=#(6/((x+4)(x-4)))-(2/((x-4)(x+3)))#
Multiply left by #((x+3)/(x+3))# and right by #((x+4)/(x+4))# (common denomanators)
=#(6(x+3))/((x+4)(x-4)(x+3)) - (2(x+4))/((x-4)(x+3)(x+4))#
Which simplifies to:
#((4x+10)/((x+4)(x-4)(x+3)))#
Please check me, but I'm not sure how you got to #((4)/((x+4)(x+3)))#
... anyway, restrictions look good though.

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