Question

Cho biểu thức A\(\frac{x\sqrt{x}+1}{x-1}-\frac{x-1}{\sqrt{x}+1}\) (với x≠1, x≥0). Rút gọn A, sau đó tính giá trị A-1 khi \(x=2016+2\sqrt{2015}\)

Answer 1

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

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

\(x=2016+2\sqrt{2015}=\left(\sqrt{2015}+1\right)^2\)

\(\Rightarrow A=\frac{\sqrt{2015}+1}{\sqrt{2015}}=\frac{2015+\sqrt{2015}}{2015}\)