Question

\(\left(\dfrac{24}{\sqrt{7}+1}+\dfrac{4}{3+\sqrt{7}}-\dfrac{3}{\sqrt{7}+2}\right)\left(4-\sqrt{7}\right)\)

Answer 1

\(\left(\dfrac{24}{\sqrt{7}+1}+\dfrac{4}{3+\sqrt{7}}-\dfrac{3}{\sqrt{7}+2}\right)\left(4-\sqrt{7}\right)\\ =\left(\dfrac{24\left(\sqrt{7}-1\right)}{7-1}+\dfrac{4\left(3-\sqrt{7}\right)}{9-7}-\dfrac{3\left(\sqrt{7}-2\right)}{7-4}\right)\left(4-\sqrt{7}\right)\\ =\left[4\left(\sqrt{7}-1\right)+2\left(3-\sqrt{7}\right)-\left(\sqrt{7}-2\right)\right]\left(4-\sqrt{7}\right)\\ =\left(4\sqrt{7}-4+6-2\sqrt{7}-\sqrt{7}+2\right)\left(4-\sqrt{7}\right)\\ =\left(4+\sqrt{7}\right)\left(4-\sqrt{7}\right)\\ =16-7=9\)