Question

A=[(\(\dfrac{x+\sqrt{9x}-1}{x+\sqrt{x}-2}\))-\(\dfrac{1}{\sqrt{x}-1}\)-\(\dfrac{1}{\sqrt{x}+2}\)]

Answer 1

\(A=\left(\dfrac{x+\sqrt{9x}-1}{x+\sqrt{x}-2}-\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}+2}\right)=\left[\dfrac{x+3\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}-\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}-\dfrac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\right]=\dfrac{x+3\sqrt{x}-1-\sqrt{x}-2-\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}=\dfrac{x+\sqrt{x}-2}{x+\sqrt{x}-2}=1\)