Answer
$\frac{90+9\sqrt{3gh}+80\sqrt{2g}+8g\sqrt{6h}}{100-3gh}$.
Work Step by Step
The given expression is
$=\frac{9+4\sqrt{8g}}{10-\sqrt{3gh}}$
$=\frac{9+4\sqrt{4\cdot 2g}}{10-\sqrt{3gh}}$
$=\frac{9+8\sqrt{ 2g}}{10-\sqrt{3gh}}$
Multiply and divide by the conjugate of the denominator.
$=\frac{9+8\sqrt{2g}}{10-\sqrt{3gh}}\cdot \frac{10+\sqrt{3gh}}{10+\sqrt{3gh}}$
Use the FOIL method.
$=\frac{90+9\sqrt{3gh}+80\sqrt{2g}+(8\sqrt{2g})\cdot (\sqrt{3gh})}{100+10\sqrt{3gh}-10\sqrt{3gh}+(-\sqrt{3gh})(\sqrt{3gh})}$
Simplify.
$=\frac{90+9\sqrt{3gh}+80\sqrt{2g}+8g\sqrt{6h}}{100-3gh}$.
