ANSWER
[tex]4(x + 6)(x - 2)[/tex]
EXPLANATION
The given rational expression is:
[tex] \frac{1}{ {x}^{2} + 4x - 12} + \frac{3x}{4x - 8} [/tex]
We can factor the denominators to obtain:
[tex] \frac{1}{(x + 6)(x - 2) } + \frac{1}{4(x - 2)} [/tex]
The common denominator is least common multiples of the denominators.
The common denominator is of the given rational expression is
[tex]4(x + 6)(x - 2)[/tex]
