Question

\(A=\dfrac{2x+2\sqrt{x}+2}{x-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\)

Rút gọn \(A=\dfrac{\sqrt{x}+3}{\sqrt{x}-1}\)

Answer 1

3. D

4. A

5. C

6. B

7. D

Answer 2

\(\Leftrightarrow A=\dfrac{2x+2\sqrt{x}+2}{\sqrt{x}^2-1}-\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

         \(=\dfrac{2x+2\sqrt{x}+2-\left(\sqrt{x}^2+1-2\sqrt{x}\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ =\dfrac{2x+2\sqrt{x}+2-x-1+2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ =\dfrac{x+4\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\=\dfrac{x+4\sqrt{x}+1}{x-1} \)