Find the value of X if \(\frac{\sqrt{2}}{x+\sqrt{2}}=\frac{1}{x-\sqrt{2}}\)

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

Simplify \(\frac{5+\sqrt{7}}{3+\sqrt{7}}\)

Rationalize \(\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}\)

Find the area of a rectangle of length 4cm and whose diagonal is 8cm, (Leave your answer in surd form)