Question

Can someone please explain how to do this problem? The websites instructions are very poor. Rewrite
`(2)/(x^(2) -x-12)` and
`(1)/(x^(2)-16 )` as equivalent rational expressions with the lowest common denominator.

Answer 1

Answer: x = -5

Explanation:

If you factor each denominator, you can find the LCM.

`(2)/(x^2-x-12)=(1)/(x^2-16)\\\\\\(2)/((x-4)(x+3))=(1)/((x-4)(x+4))\\\\\\\text{The LCM is (x-4)(x+4)(x+3)}\\\\\\(2)/((x-4)(x+3))\bigg((x+4)/(x+4)\bigg)=(1)/((x-4)(x+4))\bigg((x+3)/(x+3)\bigg)\\\\\\(2(x+4))/((x-4)(x+4)(x+3))=(1(x+3))/((x-4)(x+4)(x+3))\\`

Now that the denominators are equal, we can clear the denominator and set the numerators equal to each other.

2(x + 4) = 1(x + 3)

2x + 8 = x + 3

x + 8 = 3

x = -5