\(\dfrac{4x+1}{4\left(2-x\right)}\ge x+2\)
\(\Leftrightarrow\dfrac{4x+1}{4\left(2-x\right)}-x-2\ge0\)
\(\Leftrightarrow\dfrac{4x+1-4x\cdot\left(2-x\right)-8\left(2-x\right)}{4\left(2-x\right)}\ge0\)
\(\Leftrightarrow\dfrac{4x+1-8x+4x^2-16+8x}{4\left(2-x\right)}\ge0\)
\(\Leftrightarrow\dfrac{4x-15+4x^2}{4\left(2-x\right)}\ge0\)
\(\Leftrightarrow\dfrac{4x^2+4x-15}{4\left(2-x\right)}\ge0\)
\(\Leftrightarrow\dfrac{4x^2+10x-6x-15}{4\left(2-x\right)}\ge0\)
\(\Leftrightarrow\dfrac{2x\left(2x+5\right)-3\left(2x+5\right)}{4\left(2-x\right)}\ge0\)
\(\Leftrightarrow\dfrac{\left(2x-3\right)\left(2x+5\right)}{4\left(2-x\right)}\ge0\)
đến đây phân vế ra giải...
