Question

Cho biểu thức:

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

a) Tìm ĐKXĐ, rút gọn P

b) Tính P khi x = 9

c) Tìm x để P < \(\sqrt{P}\)

Mọi người giúp mình làm bài toán này với ạ! Mình đang cần gấp

Answer 1

a) ĐK ko bt đúng or sai

ĐKXĐ : \(\left\{{}\begin{matrix}x>=0\\x\ne0\\x\ne1\end{matrix}\right.\)

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

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

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

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

\(\dfrac{-\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}.\sqrt{x}-1\)

=\(\dfrac{-\sqrt{x}+1}{\sqrt{x}}\)

Answer 2

a: ĐKXĐ: x<>0; x<>1

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

b: Khi x=9 thì \(A=\dfrac{-1}{3\left(3-1\right)}=\dfrac{-1}{6}\)