Answer
$\frac{6-8\sqrt{30m}+3\sqrt{15}-60\sqrt{2m}}{9-480m}$.
Work Step by Step
The given expression is
$=\frac{2+\sqrt{15}}{3+4\sqrt{30m}}$
Multiply and divide by the conjugate of the denominator.
$=\frac{2+\sqrt{15}}{3+4\sqrt{30m}}\cdot \frac{3-4\sqrt{30m}}{3-4\sqrt{30m}}$
Use the FOIL method.
$=\frac{6-8\sqrt{30m}+3\sqrt{15}+(\sqrt{15})(-4\sqrt{30m})}{9-12\sqrt{30m}+12\sqrt{30m}+(4\sqrt{30m})(-4\sqrt{30m})}$
Simplify.
$=\frac{6-8\sqrt{30m}+3\sqrt{15}-60\sqrt{2m}}{9-480m}$.