Answer: x = -5
Step-by-step explanation:
If you factor each denominator, you can find the LCM.
[tex]\dfrac{2}{x^2-x-12}=\dfrac{1}{x^2-16}\\\\\\\dfrac{2}{(x-4)(x+3)}=\dfrac{1}{(x-4)(x+4)}\\\\\\\text{The LCM is (x-4)(x+4)(x+3)}\\\\\\\dfrac{2}{(x-4)(x+3)}\bigg(\dfrac{x+4}{x+4}\bigg)=\dfrac{1}{(x-4)(x+4)}\bigg(\dfrac{x+3}{x+3}\bigg)\\\\\\\dfrac{2(x+4)}{(x-4)(x+4)(x+3)}=\dfrac{1(x+3)}{(x-4)(x+4)(x+3)}\\[/tex]
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
