Question

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

a)tìm P biết |x|=1/4

b) tìm x biết P=3

Answer 1

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

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

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

|x|=1/4 nên x=1/4

Khi x=1/4 thì \(P=\dfrac{-\left(\dfrac{1}{2}-2\right)}{\dfrac{1}{4}}=-\dfrac{-3}{2}:\dfrac{1}{4}=\dfrac{3}{2}\cdot4=6\)

b: Để P=3 thì \(3x=-\sqrt{x}+2\)

=>3x+căn x-2=0

=>3x+3 căn x-2căn x-2=0

=>căn x=2/3

=>x=4/9