Question

Cho biểu thức: P = (sqrt(x))/(sqrt(x) + 3) + (3sqrt(x))/(x - 9) a) Rút gọn biểu thức P. với x>=0;x ne9 . b) Tim giá trị của x để P = 2 ,

Answer 1

a, \(P=\dfrac{\sqrt{x}}{\sqrt{x}+3}+\dfrac{3\sqrt{x}}{x-9}\)

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

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

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

\(\Rightarrow P=\dfrac{x}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+3\right)}\\ \Rightarrow P=\dfrac{x}{x-9}\)

b,Để P=2 \(\Leftrightarrow\dfrac{x}{x-9}=2\)

\(\Leftrightarrow x=2\left(x-9\right)\\ \Leftrightarrow x=2x-18\\ \Leftrightarrow x-18=0\\ \Leftrightarrow x=18\)

Answer 2