Question

Answer 1

15:

a: \(P=\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{2}{x+2\sqrt{x}}+\dfrac{x+2}{\left(\sqrt{x}-1\right)\left(x+2\sqrt{x}\right)}\)

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

\(=\dfrac{\sqrt{x}\left(x+3\sqrt{x}+2\right)}{\left(\sqrt{x}-1\right)\cdot\sqrt{x}\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)

b: Khi x=3+2căn 2 thì \(P=\dfrac{\sqrt{2}+1+1}{\sqrt{2}+1-1}=\sqrt{2}+1\)