Consider the first equation. Divide $-\frac{11}{4}$ by $\frac{\sqrt{121-112}}{4}$ by multiplying $-\frac{11}{4}$ by the reciprocal of $\frac{\sqrt{121-112}}{4}$.
$$x=\frac{-11\times 4}{4\sqrt{121-112}}$$
Cancel out $4$ in both numerator and denominator.
$$x=\frac{-11}{\sqrt{121-112}}$$
Subtract $112$ from $121$ to get $9$.
$$x=\frac{-11}{\sqrt{9}}$$
Calculate the square root of $9$ and get $3$.
$$x=\frac{-11}{3}$$
Fraction $\frac{-11}{3}$ can be rewritten as $-\frac{11}{3}$ by extracting the negative sign.