Answer
$\frac{54+43\sqrt2}{-46}$.
Work Step by Step
The given expression is
$=\frac{7+4\sqrt2}{2-5\sqrt2}$
The conjugate of the denominator is $2+5\sqrt2$.
Multiply the numerator and the denominator by $2+5\sqrt2$.
$=\frac{7+4\sqrt2}{2-5\sqrt2}\cdot \frac{2+5\sqrt2}{2+5\sqrt2}$
$=\frac{7\cdot 2+7\cdot 5\sqrt2+4\sqrt2\cdot 2+4\sqrt2\cdot 5\sqrt2}{(2)^2-(5\sqrt2)^2}$
Use the product rule.
$=\frac{14+35\sqrt2+8\sqrt2+40}{4-50}$
Add like terms.
$=\frac{54+43\sqrt2}{-46}$.
