Question

tính ( sau khi rút gọn) :

B=\(\left(\frac{1}{\sqrt{a}+\sqrt{a+1}}+\frac{1}{\sqrt{a}-\sqrt{a-1}}\right)\):\(\left(1+\sqrt{\frac{a+1}{a-1}}\right)\)với a=5

giúp với ạ cần gấp :((

Answer 1

ĐKXĐ:...

\(B=\left(\frac{\sqrt{a}-\sqrt{a+1}}{a-a-1}+\frac{\sqrt{a}+\sqrt{a-1}}{a-a+1}\right):\left(1+\frac{\sqrt{a^2-1}}{a-1}\right)\)

\(B=\left(-\sqrt{a}+\sqrt{a+1}+\sqrt{a}+\sqrt{a-1}\right).\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{a-1+\sqrt{a^2-1}}\)

\(B=\left(\sqrt{a+1}+\sqrt{a-1}\right).\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\left(\sqrt{a-1}\right)\left(\sqrt{a-1}+\sqrt{a+1}\right)}\)

\(B=\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\sqrt{a-1}}\)

\(B=\frac{\left(\sqrt{a-1}\right)^2}{\sqrt{a-1}}=\sqrt{a-1}\)

Vs a=5 có

B=\(\sqrt{5-1}=2\)