先化简，再求值：$(\frac{x^2}{x-1}-\frac{x^2}{x^2-1})÷\frac{x^2-x}{x^2-2x+1}$，其中$x$是不等式组$\left\{\begin{array}{c}x-3(x-2)⩽4,\\ \frac{2x-3}{3}<\frac{5-x}{2}\end{array}\right.$的整数解．