How do you simplify #(x^2-3x-10)/(x^2-8x+15) * (x^2+5x-6)/(x^2+4x+4)#?

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Answer 1 · 2015-05-26T21:57:19

Let's start by factoring all of the expressions:

#(x^2-3x-10)/(x^2-8x+15) * (x^2+5x-6)/(x^2+4x+4)#

#((x-5)(x+2))/((x-5)(x-3)) * ((x+6)(x-1))/((x+2)(x+2)#

We can cancel out #(x-5) and (x+2)#.

#((x+6)(x-1))/((x-3)(x+2)#

FOILing in back in gives us:

#(x^2 + 6x - x -6)/(x^2 -3x + 2x -6)#

#(x^2 + 5x -6)/(x^2 -x- 6)#