Question

P=\(\dfrac{x\sqrt{x}-47}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}-\dfrac{4\sqrt{x}+12}{\sqrt{x}+1}+\dfrac{\sqrt{x}+2}{\sqrt{x}-3}\)

a)rút gọn

b) tính GTNN

Answer 1

\(ĐKXĐ:\left\{{}\begin{matrix}x\ge0\\x\ne9\\\end{matrix}\right.\\ P=\dfrac{x\sqrt{x}+3\sqrt{x}-3x-9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\\ P=\dfrac{\sqrt{x}\left(x+3\right)-3\left(x+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\\ P=\dfrac{x+3}{\sqrt{x}+1}\)

b) \(P=\dfrac{x+3}{\sqrt{x}+1}=\dfrac{2\left(\sqrt{x}+1\right)+\left(x-2\sqrt{x}+1\right)}{\sqrt{x}+1}\\ P=2+\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}+1}\\ =>P\ge2\\ Dấubằngxảyrakhix=1\)