Question

Thu gọn P

P= \([\dfrac{2}{\sqrt{x}-1}+\dfrac{5}{\left(1-\sqrt{x}\right)\left(\sqrt{x}+2\right)}]:[1+\dfrac{3-x}{x+\sqrt{x}-2}]\)

Answer 1

đk: x \(\ge0;x\ne1\)

P = \(\left[\dfrac{2\left(\sqrt{x}+2\right)-5}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\right]:\left[1+\dfrac{3-x}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\right]\)

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

= \(\dfrac{2\sqrt{x}-1}{\sqrt{x}+1}\)