1. Ta có: $\frac{{{x}^{2}}y-xy}{x-1}=\frac{xy\left( x-1 \right)}{x-1}=x.y\ne 1$
2. Ta có: $\frac{{{x}^{2}}-{{y}^{2}}}{{{x}^{2}}+xy}=\frac{{{x}^{2}}+xy-xy-{{y}^{2}}}{{{x}^{2}}+xy}=\frac{x\left( x+y \right)-y\left( x+y \right)}{x\left( x+y \right)}$

  $=\frac{\left( x+y \right)\left( x-y \right)}{x\left( x+y \right)}=\frac{x-y}{x}$