Question

Giải các bất phương trình sau :

a) \(\dfrac{x+1}{x-1}+2>\dfrac{x-1}{x}\)

b) \(\dfrac{1}{x+1}+\dfrac{2}{x+3}< \dfrac{3}{x+2}\)

Answer 1

a) Đkxđ: \(x\ne1,x\ne0\)

\Leftrightarrow\dfrac{x+1}{x-1}+2>\dfrac{x-1}{x}\Leftrightarrow\dfrac{2}{x-1}+2>-\dfrac{1}{x}

22\Leftrightarrow\dfrac{2}{x-1}+\dfrac{1}{x}+2>0\Leftrightarrow\dfrac{2x+x-1+2\left(x^2-x\right)}{\left(x-1\right)x}=\dfrac{2x^2+x-1}{\left(x-1\right)\left(x\right)}>0

Tử {delta =9}

-1< x< \dfrac{1}{2}\Rightarrow Tử< 0

0< x< 1\Rightarrow M< 0

Nghiệm BPT là

\left[{}\begin{matrix}x< -1\\0< x< \dfrac{1}{2}\end{matrix}\right. hoặc x>1