Question

Cho biểu thức : P =( \(\sqrt{x}-\dfrac{1}{\sqrt{x}}\)):( \(\dfrac{\sqrt{x}-1}{\sqrt{x}}-\dfrac{\sqrt{x}-1}{x+\sqrt{x}}\)) với x>0:x≠1.

a) Rút gọn.

b) Tìm x sao cho P= \(\dfrac{9}{2}\)

Answer 1

a) P = \(\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}}-\frac{\sqrt{x}-1}{x+\sqrt{x}}\right)\).

P = \(\frac{\sqrt{x}.\sqrt{x}-1}{\sqrt{x}}.\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)-\sqrt{x}\left(\sqrt{x}-1\right)}\)

P = \(\frac{x-1}{\sqrt{x}}.\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{x-1-x+\sqrt{x}}\)

P = \(\frac{x-1}{\sqrt{x}}.\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\)

P = \(\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}}.\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\)

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

P = \(x-1\).

b) P = \(\frac{9}{2}\).

⇔ \(x-1=\frac{9}{2}\)

⇔ \(x=\frac{11}{2}\).

Vậy \(x=\frac{11}{2}\)thì P = \(\frac{9}{2}\).