Question

Answer 1

d: \(=\dfrac{3+2\sqrt{2}}{3-2\sqrt{2}}+\dfrac{2\sqrt{5}+3}{2\sqrt{5}-3}-\dfrac{1}{\sqrt{7}+\sqrt{5}}\)

\(=\left(3+2\sqrt{2}\right)^2+\dfrac{\left(2\sqrt{5}+3\right)^2}{20-9}-\dfrac{\sqrt{7}-\sqrt{5}}{2}\)

\(=17+12\sqrt{2}+\dfrac{29+12\sqrt{5}}{11}-\dfrac{\sqrt{7}-\sqrt{5}}{2}\)

\(=17+12\sqrt{2}+\dfrac{29}{11}+\dfrac{12}{11}\sqrt{5}-\dfrac{\sqrt{7}}{2}+\dfrac{\sqrt{5}}{2}\)

\(=\dfrac{216}{11}+12\sqrt{2}+\dfrac{35}{22}\sqrt{5}-\dfrac{1}{2}\sqrt{7}\)