Question

P=\(\sqrt{\dfrac{x+1}{\sqrt{x}-2}}\) +\(\dfrac{2\sqrt{x}}{\sqrt{x}}\)+ \(\dfrac{2+5\sqrt{x}}{4-x}\)

rút gọn

Answer 1

Đk: \(x>0;x\ne4\)

\(P=\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}}+\dfrac{2+5\sqrt{x}}{4-x}\)

\(P=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+2+\dfrac{2+5\sqrt{x}}{\left(2-\sqrt{x}\right)\left(\sqrt{x}+2\right)}\)

\(P=\dfrac{x+3\sqrt{x}+2-\left(2+5\sqrt{x}\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+2\)

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

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

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