How do you simplify the expression #((x^2-4x-32)/(x+1))/((x^2+6x+8)/(x^2-1))#?

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Answer 1 · 2016-12-26T14:38:22

The answer is #=((x-1)(x-8))/(x+2)#

Let's do some factorisations

#x^2-4x-32=(x+4)(x-8)#

#x^2+6x+8=(x+2)(x+4)#

#x^2-1=(x+1)(x-1)#

Therefore,

#((x^2-4x-32)/(x+1))/((x^2+6x+8)/(x^2-1))=(((x+4)(x-8))/((x+1)))/(((x+2)(x+4))/((x+1)(x-1))#

#=(cancel(x+4)(x-8))/(cancel(x+1))*(cancel(x+1)(x-1))/((x+2)cancel(x+4))#

#=((x-1)(x-8))/(x+2)#