Question

\(p=\dfrac{\sqrt{x}-2}{x-1}-\dfrac{\sqrt{x}+2}{x+2\sqrt{x}+1}:\left(\dfrac{2}{x^2-2x+1}\right)\)với x\(\ge0;x\ne1\)

1 .rút gọn p

2.tính giá trị của p khi x=7-\(4\sqrt{3}\)

3 . tính GTLN của p

Answer 1

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

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

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

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

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

\(P=\dfrac{2\sqrt{x}-4}{2\left(x-1\right)}-\dfrac{\left(x\sqrt{x}-3\sqrt{x}+2\right)\left(x-1\right)}{2\left(x-1\right)}\)

\(P=\dfrac{2\sqrt{x}-4}{2\left(x-1\right)}-\dfrac{x^2\sqrt{x}-x\sqrt{x}-3x\sqrt{x}+3\sqrt{x}+2x-2}{2\left(x-1\right)}\)