Answer
The answer is $-12$.
Work Step by Step
We insert $x = -\frac{3}{4}$ in $\frac{4}{1 + \frac{1}{x}}$:
$\frac{4}{1 + \frac{1}{x}} = \frac{4}{1 + \frac{1}{-\frac{3}{4}}} = \frac{4}{1 - \frac{1}{\frac{3}{4}}} = \frac{4}{1 - (1 \div \frac{3}{4})} = \frac{4}{1 - (1 \cdot \frac{4}{3})} = \frac{4}{1 - \frac{4}{3}} = \frac{4}{\frac{3}{3} - \frac{4}{3}} = \frac{4}{ \frac{3 - 4}{3}} = \frac{4}{ \frac{- 1}{3}} = - \frac{4}{ \frac{ 1}{3}} = - 4 \div \frac{1}{3} = -4 \cdot 3 = -12$.
