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

Question

1442 views around the world

You can reuse this answer
Creative Commons License

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,

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

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

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

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