Question

Solve: $\frac{3x+1}{2}-\frac{4}{x-1}=x+2$

Answer 1

$\frac{3x+1}{2}-\frac{4}{x-1}=x+2$

$\Rightarrow \frac{(3x+1)(x-1)-8}{2(x-1)}=x+2$

$\Rightarrow (3x+1)(x-1)-8=2(x+2)(x-1)$

$\Rightarrow 3x^2-3x+x-1-8=2[x^2-x+2x-2]$

$\Rightarrow 3x^2-2x-9=2x^2-2x+4x-4$

$\Rightarrow 3x^2-2x-9=2x^2+2x-4$

$\Rightarrow 3x^2-2x-9-2x^2-2x+4=0$

$\Rightarrow x^2-4x-5=0$

$\Rightarrow x^2-5x+x-5=0$

$\Rightarrow x(x-5)+1(x-5)=0$

$\Rightarrow (x-5)(x+1)=0$

$\therefore x=5,-1$