Answer
$a=-\displaystyle \frac{1}{2}$ and $b=-\displaystyle \frac{1}{4}$
Work Step by Step
We are given:
$2\lt x\lt 4$
We subtract $6$:
$2-6\lt x-6\lt 4-6$
$-4\lt x-6\lt -2$
We take the reciprocal:
$-\frac{1}{4}\gt \frac{1}{x-6}\gt -\frac{1}{2}$
$-\frac{1}{2}\lt \frac{1}{x-6}\lt -\frac{1}{4}$
Therefore:
$a=-\displaystyle \frac{1}{2}$ and $b=-\displaystyle \frac{1}{4}$