What is the simplified form of #(x-3)/(x^2+x-12) * (x+4)/(x^2 + 8x + 16)#?

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Answer 1 · 2018-06-12T03:53:46

#1/(x+4)^2#

First, factor the fractions:

#(x-3)/(x^2+x-12) * (x+4)/(x^2+8x+16)#

#(x-3)/((x-3)(x+4)) * (x+4)/((x+4)(x+4))#

Now, combine them:

#((x-3)(x+4))/((x-3)(x+4)^3)#

#(cancel((x-3))cancel((x+4)))/(cancel((x-3))(x+4)^(cancel3 color(white)"." color(red)2))#

#1/(x+4)^2#

Or if you want to expand it back out:

#1/(x^2+8x+16)#

Final Answer