Question

Can someone please explain how to do this problem? The websites instructions are very poor. Rewrite et/?f=%5Cfrac%7B2%7D%7Bx%5E%7B2%7D%20-x-12%7D" id="TexFormula1" title="\frac{2}{x^{2} -x-12}" alt="\frac{2}{x^{2} -x-12}" align="absmiddle" class="latex-formula"> and $\frac{1}{x^{2}-16 }$ as equivalent rational expressions with the lowest common denominator.

Answer 1

Answer: x = -5

Step-by-step explanation:

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

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

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