Solve $(x+2)/(x-1)=x/2$, where $x$ ≠ 1.

Cross-multiplying: $2(x+2)=x(x-1)$, so $2x+4=x^2-x$ and $x^2-3x-4=0.x=\frac{3\pm \sqrt{9+16}}{2}=\frac{3\pm 5}{2}=4$ or −1. Both check: $(4+2)/(4-1)=2=4/2$, and $(-1+2)/(-1-1)=-\frac{1}{2}=-1/2$. Multiplying only the numerator across gives $x^2-2x-2=0$ and the wrong surd answer $1\pm \sqrt{3}$.