Answer
$a=\displaystyle \frac{1}{4}$ and $b=1$
Work Step by Step
We are given:
$-3\lt x\lt 0$
We add $4$:
$-3+4\lt x+4\lt 0+4$
$1\lt x+4\lt 4$
We take the reciprocal:
$1\gt \frac{1}{x+4}\gt \frac{1}{4}$
$\frac{1}{4}\lt \frac{1}{x+4}\lt 1$
Therefore:
$a=\displaystyle \frac{1}{4}$ and $b=1$
