Answer
x = $ 9+3 \sqrt 10 + 6 \sqrt 2 + 2 \sqrt 20$
Work Step by Step
$\frac{2 + \sqrt 2}{2 + \sqrt 2} = \frac{x}{3 + \sqrt 10}$
We cross multiply the fraction
$\frac{(2 + \sqrt 2)(3 + \sqrt 10)}{2 + \sqrt 2} = x$
We simplify the top by using FOIL. FOIL: First (Multiply the first variables in the brackets), outside (Multiply the outer variables), Inside (Multiply the inside variables), Last (Multiply the last variables in the brackets).
$ \frac{6 + 3\sqrt 2 + 2\sqrt 10 + \sqrt 20}{2 + \sqrt 2}$ = x
We simplify the denominator and numerator.
$x = (3)(3) + (3)(\sqrt 10) + (6)(\sqrt 2) + 2(\sqrt 20)$
We add the radicals with the same numbers and the constants together
x = $ 9+3 \sqrt 10 + 6 \sqrt 2 + 2 \sqrt 20$
