Question

Bài 5: Cho biểu thức: \(P=\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}+\frac{2+5\sqrt{x}}{4-x}\)

a) Tìm ĐKXĐ

b) Rút gọn P

c) Tìm x để P=2

Answer 1

https://i.imgur.com/xjq2J5w.jpg

Answer 2

https://i.imgur.com/0t5vjlL.jpg

Answer 3

ĐKXĐ: \(x\ge0;x\ne4\)

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

\(=\frac{x+3\sqrt{x}+2+2x-4\sqrt{x}-5\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{3x-6\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{3\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{3\sqrt{x}}{\sqrt{x}+2}\)

\(P=2\Rightarrow\frac{3\sqrt{x}}{\sqrt{x}+2}=2\Rightarrow3\sqrt{x}=2\sqrt{x}+4\)

\(\Rightarrow\sqrt{x}=4\Rightarrow x=16\)