[tex]\bold{a)} \ \frac{x^2-1}{xy^2}\cdot \frac{x^2y}{1+x}=\frac{(x+1)(x-1)}{y}\cdot \frac{x}{1+x}=\frac{x-1}{y}\cdot \frac{x}{1}=\frac{x(x-1)}{y}=\boxed{\bold{\frac{x^2-x}{y}}}; \\ \\ \bold{b)} \ \frac{x^2-y^2}{2xy}\cdot \frac{2x}{x+y}=\frac{(x+y)(x-y)}{y}\cdot \frac{1}{x+y}=\frac{x-y}{y} \cdot \frac{1}{1}=\boxed{\bold{\frac{x-y}{y}}}}.[/tex]
