Question

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

1. rút gọn A

2. Tìm các số nguyên y để biểu thức A khi có giá trị nguyên

Answer 1

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