How do you simplify #(x^2 – 6x – 7 )/( x^2 – 1)#?

1 Answer
Oct 7, 2015

Answer:

#(x-7)/(x-1)#

Explanation:

Notice that you can rewrite the numerator of the fraction as

#x^2 - 6x - 7 = x^2 - 7x + x - 7#

#=x(x-7) + (x-7) = (x-7)(x+1)#

The denominator of the fraction can be rewritten as

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

This means that the expression becomes

#( cancel((x+1)) * (x-7))/(cancel((x+1)) * (x-1)) = color(green)((x-7)/(x-1))#