Question

rút gọn biểu thức

giúp em với ạ, em cảm ơn

Answer 1

a: \(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}\)

\(=\dfrac{\sqrt{100}+\sqrt{40}}{\sqrt{5}+\sqrt{2}}\)

\(=\dfrac{\sqrt{20}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{5}+\sqrt{2}}=\sqrt{20}=2\sqrt{5}\)

c: \(\dfrac{\sqrt{2}}{\sqrt{5}-\sqrt{3}}\)

\(=\dfrac{\sqrt{2}\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)}\)

\(=\dfrac{\sqrt{10}+\sqrt{6}}{5-3}=\dfrac{\sqrt{10}+\sqrt{6}}{2}\)

e: \(\left(\dfrac{15}{\sqrt{6}+1}+\dfrac{4}{\sqrt{6}-2}-\dfrac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)

\(=\left(\dfrac{15\left(\sqrt{6}-1\right)}{6-1}+\dfrac{4\left(\sqrt{6}+2\right)}{6-4}-\dfrac{12\left(3+\sqrt{6}\right)}{9-6}\right)\cdot\left(\sqrt{6}+11\right)\)

\(=\left[3\left(\sqrt{6}-1\right)+2\left(\sqrt{6}+2\right)-4\left(3+\sqrt{6}\right)\right]\left(\sqrt{6}+11\right)\)

\(=\left(3\sqrt{6}-3+2\sqrt{6}+4-12-4\sqrt{6}\right)\left(\sqrt{6}+11\right)\)

\(=\left(\sqrt{6}-11\right)\left(\sqrt{6}+11\right)\)

=6-121

=-115

g: \(\dfrac{1}{\sqrt{5}+1}+\dfrac{1}{\sqrt{5}-2}-\dfrac{1}{3-\sqrt{5}}-\sqrt{5}\)

\(=\dfrac{\sqrt{5}-1}{4}+\dfrac{\sqrt{5}+2}{1}-\dfrac{1\left(3+\sqrt{5}\right)}{4}-\sqrt{5}\)

\(=\dfrac{1}{4}\sqrt{5}-\dfrac{1}{4}+\sqrt{5}+2-\dfrac{3}{4}-\dfrac{\sqrt{5}}{4}-\sqrt{5}\)

\(=-1+2=1\)