Question

Rút gọn biểu thức( không dùng máy tính). a) \(2\sqrt{50}-\sqrt{18}\) b) P= \(\left(\frac{1}{\sqrt{a}-1}+\frac{1}{\sqrt{a}+1}\right)\div\frac{1}{a-1}\)với a≥0, a≠1

Answer 1

\(a.2\sqrt{50}-\sqrt{18}=2\sqrt{25\cdot2}-\sqrt{9\cdot2}=10\sqrt{2}-3\sqrt{2}=7\sqrt{2}\)

b.

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