Question

What is the simplified form of x minus 4 over x squared minus x minus 12 ⋅ x minus 4 over x squared minus 8x plus 16 ?

Answer 1

`(1)/((x+3)(x-4))`

Explanation:

The expression we are given is

`(x-4)/(x^2-x-12)* (x-4)/(x^2-8x+16)`

We factor the denominator of each expression.

To factor

x²-x-12, we find factors of -12 that sum to -1.

-4(3) = -12 and -4+3 = -1; this gives us

`(x-4)/((x-4)(x+3))`

Cancelling the common factors in the numerator and denominator, we have

`(1)/(x+3)`

To factor

x²-8x+16, we find factors of 16 that sum to -8;

-4(-4) = 16 and -4+-4 = -8. This gives us

`(x-4)/((x-4)(x-4))`

Cancelling the common factors in the numerator and denominator, we have

`(1)/(x-4)`

This gives us

`(1)/(x+3)* (1)/(x-4)\\\\=(1)/((x+3)(x-4))`

Answer 2

1 / (x + 3)(x + 4)

That is, 1 over the quantity x plus 3 times the quantity x minus 4.

Step by step explanation

The given expression =
`(x-4)/(x^2 - x - 12) . (x-4)/(x^2 - 8x + 16)`

Let's factor the denominators.

=
`(x-4)/((x - 4)(x + 3)) .(x-4)/((x - 4)(x - 4))`

Cancelling (x- 4) both in the numerator and the denominator, we get

=
`(1)/((x + 3)) .(1)/((x- 4))`

= 1/(x + 3)(x - 4)

The answer is 1 over the quantity x plus 3 times the quantity x minus 4.

Thank you.