Question

Solve:
$\left|\begin{array}{ccc}1& 1& 2\\ 1& -2& 3\\ 1& (x+1)& x\end{array}\right|=0$

Answer 1

$1(-2x-3x-3)-(4x-2x-2)+(3+4)=0$

$-2-5x-3+x+2+7=0$

$-4x=-6$

$x=\frac{3}{2}$