Question

cho biểu thức P=(\(\left(\dfrac{3x+3}{x\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\right):\left(\dfrac{2x-5\sqrt{x}+5}{\sqrt{x}-1}\right)\)

a) rút gọn P

Answer 1

đk x \(\ne1;x>0\)

\(p=\left(\dfrac{3x+3}{\sqrt{x^3}-1}-\dfrac{\sqrt{x}-1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\right):\left(\dfrac{2x-5\sqrt{x}+5}{\sqrt{x}-1}\right)\\ =\left(\dfrac{3x+3-\left(\sqrt{x}-1\right)^2-x-\sqrt{x}-1}{\sqrt{x^3}-1}\right).\left(\dfrac{\sqrt{x}-1}{2x-5\sqrt{x}+5}\right)\\ =\dfrac{3x+3-x+2\sqrt{x}-1-x-\sqrt{x}-1}{\sqrt{x^3}-1}.\dfrac{\sqrt{x}-1}{2x-5\sqrt{x}+5}\\ =\dfrac{x+\sqrt{x}+1}{x+\sqrt{x}+1}.\dfrac{1}{2x-5\sqrt{x}+5}\\ =\dfrac{1}{2x-5\sqrt{x}+5}\)