Giải bpt tích, bpt thương

`\frac{-3x+1}{2x+1}<-2` `(`ĐK : `x ne -1/2``)`

`<=>\frac{3x+1}{2x+1}>2`

`<=>(3x-1)/(2x+1)-2>0`

`<=>-(x+3)/(2x+1)>0`

`<=>(x+3)/(2x+1)<0`

`<=>`$\left[\begin{matrix} \begin{cases} x+3>0\\2x+1<0 \end{cases}\\ \begin{cases} x+3<0\\2x+1>0 \end{cases}\end{matrix}\right.$

`<=>`$\left[\begin{matrix} \begin{cases} x>-3\\x<-\frac{1}{2} \end{cases}\\ \begin{cases} x<-3\\x>-\frac{1}{2} \end{cases}\end{matrix}\right.$`=>{(-3<x<1/2),(x in emptyset):}=>-3<x<1/2`

Vậy `...`

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`(x+9)/(x-1)>5` `(`ĐK : `xne1)`

`<=>(x+9)/(x-1)-5>0`

`<=>(-4x+14)/(x-1)>0`

`<=>(4x-14)/(x-1)<0`

`<=>`$\left[\begin{matrix} \begin{cases} 4x-14>0\\x-1<0 \end{cases}\\ \begin{cases} 4x-14<0\\x-1>0 \end{cases}\end{matrix}\right.$

`<=>`$\left[\begin{matrix} \begin{cases} x>\frac{7}{2}\\x<1 \end{cases}\\ \begin{cases} x<\frac{7}{2}\\x>1 \end{cases}\end{matrix}\right.$`=>{(x in emptyset), (1<x<7/2):}=>1<x<7/2`

Vậy `...`