Question

rút gọn các biểu thức

a)P=\(\dfrac{1}{\sqrt{5}-2}+\dfrac{1}{\sqrt{5}+2}\)

b)Q=\(\left(1+\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right).\dfrac{1}{\sqrt{x}}\) với x>0, x\(\ne\)1

Answer 1

a) \(P=\dfrac{1}{\sqrt{5}-2}+\dfrac{1}{\sqrt{5}+2}=\dfrac{\sqrt{5}+2+\sqrt{5}-2}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}=\dfrac{2\sqrt{5}}{\left(\sqrt{5}\right)^2-2^2}=2\sqrt{5}\)

b)\(Q=\left(1+\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right)\cdot\dfrac{1}{\sqrt{x}}=\dfrac{\sqrt{x}-1+\sqrt{x}+1}{\sqrt{x}-1}\cdot\dfrac{1}{\sqrt{x}}\)

\(Q=\dfrac{2\sqrt{x}}{\sqrt{x}-1}\cdot\dfrac{1}{\sqrt{x}}=\dfrac{2}{\sqrt{x}-1}\)

Tick hộ nha