# How do you rationalize (3sqrt7) /( 5-sqrt7)?

You can rationalize $\frac{3 \sqrt{7}}{5 - \sqrt{7}}$ by multiplying both the numerator and the denominator with the the denominator's conjugate
In this case, the denominator's conjugate is $\sqrt{7} + 5$:
$\frac{3 \sqrt{7} \cdot \left(\sqrt{7} + 5\right)}{5 - \sqrt{7} \cdot \left(\sqrt{7} + 5\right)}$
This means the rationalized answer is $\frac{15 \sqrt{7} + 21}{18}$