Question

Which expression is equivalent to x^2+7x+12/x^2-x-12?

A)x+3/x-3
B)x+4/x-4
C)(x+3)(x+4)/(x-3)(x-4)
D)-1/1

Answer 1

x^2+7x+12/x^2-x-12
x^2+4x+3x+12/x^2+3x-4x-12
x * (x+4) +3(x+4)/ x* (x+3)-4(x+3)
(x+3)(x+4)/(x-4)(x+3)

x+4/x-4

Answer 2

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

Explanation:

Given :
`(x^2+7x+12)/(x^2-x-12)`

Solution:

`(x^2+7x+12)/(x^2-x-12)`

Factorize the numerator and denominator.

`(x^2+3x+4x+12)/(x^2-4x+3x-12)`

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

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

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

So,
`(x^2+7x+12)/(x^2-x-12)` =
`((x+4))/((x-4))`

Hence Option B is correct.