Question

Cho biểu thức:

P=\(\dfrac{1}{\sqrt{x}-2}+\dfrac{2}{\sqrt{X}+2}-\dfrac{2\sqrt{X}}{x-4}\) a) Tìm điều kiện để P xác định

b) rút gọn biểu thức P

Answer 1

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

a) \(ĐKXĐ:x\ge0;x\ne4\)

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

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

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

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

\(=\dfrac{\sqrt{x}+2+2\sqrt{x}-4-2\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

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

\(=\dfrac{1}{\sqrt{x}+2}\)

Vậy: \(P=\dfrac{1}{\sqrt{x}+2}\)

_Chúc bạn học tốt_