Rationalize the denominator of the expression.

Question

Quizplus · Accepted Answer

To rationalize the denominator, we need to multiply both the numerator and denominator by a conjugate of the denominator. The conjugate of $\sqrt{b^2-4ac}$ is $\sqrt{b^2-4ac}$. So, multiplying the numerator and denominator by $\sqrt{b^2-4ac}$, we get:

$\frac{a}{\sqrt{b^2-4ac}} \cdot \frac{\sqrt{b^2-4ac}}{\sqrt{b^2-4ac}} = \frac{a\sqrt{b^2-4ac}}{b^2-4ac}$

So, the expression becomes:

$\frac{-2a + a\sqrt{b^2-4ac}}{b^2-4ac}$

which matches choice C.

Rationalize the Denominator of the Expression