Question

\(\dfrac{5}{\sqrt{7}+\sqrt{2}}-\dfrac{6}{\sqrt{7}-1}+\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\)

Answer 1

\(\dfrac{5}{\sqrt{7}+\sqrt{2}}-\dfrac{6}{\sqrt{7}-1}+\dfrac{2-\sqrt{2}}{\sqrt{2}-1}=\dfrac{5\left(\sqrt{7}-\sqrt{2}\right)}{\left(\sqrt{7}+\sqrt{2}\right)\left(\sqrt{7}-\sqrt{2}\right)}-\dfrac{6\left(\sqrt{7}+1\right)}{\left(\sqrt{7}-1\right)\left(\sqrt{7}+1\right)}+\dfrac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}=\dfrac{5\left(\sqrt{7}-\sqrt{2}\right)}{7-2}-\dfrac{6\left(\sqrt{7}+1\right)}{7-1}+\sqrt{2}=\dfrac{5\left(\sqrt{7}-\sqrt{2}\right)}{5}-\dfrac{6\left(\sqrt{7}+1\right)}{6}+\sqrt{2}=\sqrt{7}-\sqrt{2}-\left(\sqrt{7}+1\right)+\sqrt{2}=\sqrt{7}-\sqrt{2}-\sqrt{7}-1+\sqrt{2}=-1\)