Answer
$\frac{4-2\sqrt{30x}+8\sqrt{5x}-20x\sqrt{6}}{2-15x}$.
Work Step by Step
The given expression is
$=\frac{4+8\sqrt{5x}}{2+\sqrt{30x}}$
Multiply and divide by the conjugate of the denominator.
$=\frac{4+8\sqrt{5x}}{2+\sqrt{30x}}\cdot \frac{2-\sqrt{30x}}{2-\sqrt{30x}}$
Use the FOIL method.
$=\frac{8-4\sqrt{30x}+16\sqrt{5x}+(8\sqrt{5x})\cdot (-\sqrt{30x})}{4-2\sqrt{30x}+2\sqrt{30x}+(\sqrt{30x})(-\sqrt{30x})}$
Simplify.
$=\frac{8-4\sqrt{30x}+16\sqrt{5x}-40x\sqrt{6}}{4-30x}$
Divide the numerator and the denominator by $2$.
$=\frac{4-2\sqrt{30x}+8\sqrt{5x}-20x\sqrt{6}}{2-15x}$.
