Question

giải hộ mk con này vs mk 2 like cho: rút gọn

:\(P1=\frac{1+\sqrt{5}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}+\frac{1-\sqrt{5}}{\sqrt{2}-\sqrt{3}-\sqrt{5}}\)

\(P2=\left(\frac{1-A\sqrt{A}}{1-\sqrt{A}}+\sqrt{A}\right)\cdot\left(\frac{1-\sqrt{A}}{1-A}\right)^2\)

 

Answer 1

P2\(=\left(\frac{1-A\sqrt{A}}{1-\sqrt{A}}+\sqrt{A}\right).\left(\frac{1-\sqrt{A}}{1-A}\right)^2\)\(=\left(\frac{1-A\sqrt{A}+\sqrt{A}-A}{1-\sqrt{A}}\right).\frac{\left(1-\sqrt{A}\right)^2}{\left(1-A\right)^2}\)\(=\frac{\left(\sqrt{A}+1\right)\left(1-A\right)}{1-\sqrt{A}}.\frac{\left(1-\sqrt{A}\right)^2}{\left(1-\sqrt{A}\right)^2\left(1+\sqrt{A}\right)^2}\)

\(=\left(\sqrt{A}+1\right)^2.\frac{1}{\left(1+\sqrt{A}\right)^2}=1\)