Question

Thực hiện các phép tính sau:

a) \(\dfrac{\sqrt{7}-5}{2}-\dfrac{6-2\sqrt{7}}{4}+\dfrac{6}{\sqrt{7}-2}-\dfrac{5}{4+\sqrt{7}}\)

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

Answer 1

a,

\(\dfrac{\sqrt{7}-5}{2}-\dfrac{6-2\sqrt{7}}{4}+\dfrac{6}{\sqrt{7}-2}-\dfrac{5}{4+\sqrt{7}}\)

\(=\dfrac{\sqrt{7}-5}{2}-\dfrac{3-\sqrt{7}}{2}+\dfrac{6\sqrt{7}+12}{3}-\dfrac{20-5\sqrt{7}}{9}\)

\(=\dfrac{2\sqrt{7}-8}{2}+\dfrac{18\sqrt{7}+36}{9}-\dfrac{20-5\sqrt{7}}{9}\)

\(=\sqrt{7}-4+\dfrac{23\sqrt{7}+16}{9}\)

\(=\dfrac{9\sqrt{7}-36}{9}+\dfrac{23\sqrt{7}+16}{9}=\dfrac{32\sqrt{7}-20}{9}\)