Answer
$\frac{21-35\sqrt{15ab}-18\sqrt{3ab}+90\sqrt{5}ab}{9-375ab}$.
Work Step by Step
The given expression is
$=\frac{7-6\sqrt{3ab}}{3+5\sqrt{15ab}}$
Multiply and divide by the conjugate of the denominator.
$=\frac{7-6\sqrt{3ab}}{3+5\sqrt{15ab}}\cdot \frac{3-5\sqrt{15ab}}{3-5\sqrt{15ab}}$
Use the FOIL method.
$=\frac{21-35\sqrt{15ab}-18\sqrt{3ab}+(-6\sqrt{3ab})\cdot (-5\sqrt{15ab})}{9-15\sqrt{15ab}+15\sqrt{15ab}+(5\sqrt{15ab})(-5\sqrt{15ab})}$
Simplify.
$=\frac{21-35\sqrt{15ab}-18\sqrt{3ab}+90\sqrt{5}ab}{9-375ab}$.
