If $\frac{1+\sqrt{2}}{1-\sqrt{2}}$is expressed in the form $x+y\sqrt{2}$, find the values of x and y

Find y, if $\sqrt{12}-\sqrt{147}+y\sqrt{3}=0$

Rationalize $\frac{2}{6-5\sqrt{3}}$

Simplify $\frac{\sqrt{12}-\sqrt{3}}{\sqrt{12}+\sqrt{3}}$

Simplify $\frac{1}{\sqrt{3}+2}$

Simplify $\frac{\sqrt{98}-\sqrt{50}}{\sqrt{32}}$

Simplify ${{(\sqrt{0.7}+\sqrt{70})}^{2}}$

Given that $p=1+\sqrt{2}\text{ and }q=1-\sqrt{2}$ evaluate $\frac{{{p}^{2}}-{{q}^{2}}}{2pq}$

if $\frac{2\sqrt{3}-2}{\sqrt{3}+2\sqrt{2}}=m+n\sqrt{6}$. If the value of m and n respectively