Question

Giúp em với !!!!!!!

Answer 1

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

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

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

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

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

\(\Rightarrow P=\dfrac{x}{\sqrt{x}-1}\)

Answer 2

\(P=4\\ \Rightarrow\dfrac{x}{\sqrt{x}-1}=4\\ \Rightarrow x=4\sqrt{x}-4\\ \Rightarrow x+4=4\sqrt{x}\\ \Rightarrow x^2+8x+16=16x\\ \Rightarrow x^2-8x+16=0\\ \Rightarrow\left(x-4\right)^2=0\\ \Rightarrow x=4\)