Question

cho bỉểu thức

A=\(\left(\frac{y\sqrt{y}-1}{y-\sqrt{y}}-\frac{y\sqrt{y}+1}{y+\sqrt{y}}\right):\frac{2\left(y-2\sqrt{y}+1\right)}{y-1}\) rút gọn biểu thức trên

Answer 1

ĐKXĐ: \(y>0;y\ne1\)

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

\(A=\left(\frac{y+\sqrt{y}+1}{\sqrt{y}}-\frac{y-\sqrt{y}+1}{\sqrt{y}}\right)\frac{\sqrt{y}+1}{2\left(\sqrt{y}-1\right)}\)

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

Answer 2