Question

D=\(\dfrac{2\sqrt{x}-9}{x-\sqrt{x}+6}-\dfrac{\sqrt{x}+3}{\sqrt{x}-2}-\dfrac{2\sqrt{x}+1}{3-\sqrt{x}}\)

rút gọn ,tìm x để D<1

Answer 1

Sửa đề: \(D=\dfrac{2\sqrt{x}-9}{x-\sqrt{x}-6}-\dfrac{\sqrt{x}+3}{\sqrt{x}+2}-\dfrac{2\sqrt{x}+1}{3-\sqrt{x}}\)

\(D=\dfrac{2\sqrt{x}-9-\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)+\left(2\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{2\sqrt{x}-9-x+9+2x+5\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{x+7\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}\)