Given \( \frac{1}{(\sqrt{2}-1)^{2}} \), express in the form \( \mathrm{p}+\mathrm{q} \sqrt{2} \) such that p and q are constants (4 Marks)

ii) \( \frac{4 x^{2}+3 x+7}{x+1} \)

\( \therefore \sqrt { x } ( x ^ { \frac { 5 } { 2 } } + x ^ { 2 } + 5 ) \)

2imalify \( \frac{x^{2}-y^{2}}{x^{2} x y} \) \( \frac{y+2 x-3 y}{3 x-2 y}=4 \), evaluate \( 2 x y \) If \( z=\sqrt{x^{2}-y^{2}} \), express \( x \) interm 9 \( y \) and 2

\( x = \frac { - ( - 1 ) \pm \sqrt { - 79 } } { 2.1 } \)

5. Separen en términos y resuelvan. a. \( \left(-\frac{4}{3}+\frac{1}{6}\right)-\left(-\frac{3}{2}\right)^{-2}+\sqrt[3]{\left(\frac{3}{4}+\frac{1}{8}\right)-} \) b. \( \left(\frac{3}{2}-\frac{1}{2}\right)^{2}+\sqrt[3]{-\frac{1}{64}}-0.5= \) c. \( \sqrt[3]{1-\frac{7}{8}}-\left(-\frac{2}{5}+\frac{1}{10}\right)^{-4}+0.3- \) d. \( -\left(\frac{8}{5}-\frac{6}{15}\right)-\sqrt[3]{1-\frac{31}{32}}+\left(\frac{7}{5}\right)^{2}= \)