Question

Rút gọn các biểu thức sau A= \(\sqrt{112}-\sqrt{45}-\sqrt{63}+2\sqrt{20}\) B= \(\left(1+\frac{x+\sqrt{x}}{1+\sqrt{x}}\right)\left(1+\frac{x-\sqrt{x}}{1-\sqrt{x}}\right)\)với 0≤x≠1

Answer 1

\(A=\sqrt{112}+2\sqrt{20}-\left(\sqrt{45}+\sqrt{63}\right)=4\sqrt{7}+4\sqrt{5}-3\sqrt{5}-3\sqrt{7}=4\left(\sqrt{7}+\sqrt{5}\right)-3\left(\sqrt{7}+\sqrt{5}\right)=\sqrt{7}+\sqrt{5}\)

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