Rút gọn phân thức:

a) $\frac{6x^2{y}^2}{8x{y}^5}$;                                            b) $\frac{10x{y}^2(x+y)}{15xy{(x+y)}^3}$;

c) $\frac{2x^2+2x}{x+1}$;                                         d) $\frac{x^2-xy-x+y}{x^2+xy-x-y}$.

Giải

a) $\frac{6x^2{y}^2}{8x{y}^5}=\frac{3x.2x{y}^2}{4y^3.2x{y}^2}=\frac{3x}{4y^3}$;

b) $\frac{10x{y}^2(x+y)}{15xy{(x+y)}^3}=\frac{2x.5xy(x+y)}{3{(x+y)}^2.5xy(x+y)}=\frac{2x}{3{(x+y)}^2}$;

c) $\frac{2x^2+2x}{x+1}=\frac{2x\left(x+1\right)}{x+1}=2x$;

d) $\frac{x^2-xy-x+y}{x^2+xy-x-y}=\frac{x\left(x-y\right)-\left(x-y\right)}{x\left(x+y\right)-\left(x+y\right)}=\frac{\left(x-y\right)\left(x-1\right)}{\left(x+y\right)\left(x-1\right)}=\frac{x-y}{x+y}$.