How do you simplify #(8-x)/(x^2-7x-8)#?

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Answer 1 · 2018-03-22T12:08:45

#-1/(x+1)#

Lets begin by factoring the quadratic in the denominator:

#x^2-7x-8=(x-8)(x+1)#

The first factor is, in fact, the negative of the numerator:

#8-x = -(x-8)#

So we can rewrite our fraction as:

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

Finally

#-1/(x+1)#