Answer
Michelle should multiply and divide by the conjugate.
The correct answer is $\frac{48-12\sqrt5 x}{16-5 x}$.
Work Step by Step
The given expression is
$=\frac{12}{4+\sqrt{5 x}}$
Multiply the numerator and the denominator by the conjugate of the denominator.
$=\frac{12}{4+\sqrt{5 x}}\cdot \frac{4-\sqrt{5 x}}{4-\sqrt{5 x}}$
Use distributive property and the FOIL method.
$=\frac{48-12\sqrt{5 x}}{16-4\sqrt{5 x}+4\sqrt{5 x}-(\sqrt{5 x})(\sqrt{5 x})}$
Simplify.
$=\frac{48-12\sqrt5 x}{16-5 x}$.
