Question

[Như Ngọc]

Giải các bất phương trình

a.\(\frac{3}{1-x}\ge\frac{5}{2x+1}\)

b.\(\frac{\left(2x-1\right)\left(2-x\right)}{x^2-4x+3}< 0\)

Answer 1

[Nguyễn Việt Lâm]

a/ \(\frac{3}{1-x}-\frac{5}{2x+1}\ge0\Leftrightarrow\frac{11x-2}{\left(1-x\right)\left(2x+1\right)}\ge0\Rightarrow\left[{}\begin{matrix}x< -\frac{1}{2}\\\frac{2}{11}\le x< 1\end{matrix}\right.\)

b/ \(\frac{\left(2x-1\right)\left(2-x\right)}{\left(x-1\right)\left(x-3\right)}< 0\Rightarrow\left[{}\begin{matrix}x>3\\1< x< 2\\x< \frac{1}{2}\end{matrix}\right.\)