Giải phương trình : x+10/x^2-x-2 + 3/x+1 – 2/2-x = 1

`\frac{x+10}{x^2-x-2}+\frac{3}{x+1}-\frac{2}{2-x}=1` `(x ne -1; x ne 2)`

`⇔\frac{x+10}{x^2-2x+x-2}+\frac{3}{x+1}+\frac{2}{x-2}=1`

`⇔\frac{x+10}{x(x-2)+(x-2)}+\frac{3}{x+1}+\frac{2}{x-2}=1`

`⇔\frac{x+10+3(x-2)+2(x+1)}{(x+1)(x-2)}=\frac{(x+1)(x-2)}{(x+1)(x-2)}`

`⇒x+10+3(x-2)+2(x+1)=(x+1)(x-2)`

`⇔x+10+3x-6+2x+2=x^2-2x+x-2`

`⇔-x^2+7x+8=0`

`⇔x^2-7x-8=0`

`⇔x^2+x-8x-8=0`

`⇔x(x+1)-8(x+1)=0`

`⇔(x-8)(x+1)=0`

`⇔` \(\left[ \begin{array}{l}x-8=0\\x+1=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=8(tm)\\x=-1(ktm)\end{array} \right.\)