Thực hiện các phép tính sau:

a) $\frac{15x}{7y^3}.\frac{2y^2}{x^2};$                             b) $\frac{4y^2}{11x^4}.\left(-\frac{3x^2}{8y}\right)$;                         c) $\frac{x^3-8}{5x+20}.\frac{x^2+4x}{x^2+2x+4}$.

Giải     

a) $\frac{15x}{7y^3}.\frac{2y^2}{x^2}=\frac{15x.2y^2}{7y^3{x}^2}=\frac{30x{y}^2}{7x^2{y}^3}=\frac{30}{7xy}$.

b) $\frac{4y^2}{11x^4}.\left(-\frac{3x^2}{8y}\right)=-\frac{4y^2}{11x^4}.\frac{3x^2}{8y}=-\frac{4y^2.3x^2}{11x^4.8y}=-\frac{3x^2{y}^2}{11.2.x^{4}y}=-\frac{3y}{22x^2}$

c) $\frac{x^3-8}{5x+20}.\frac{x^2+4x}{x^2+2x+4}=\frac{\left(x^3-8\right)\left(x^2+4x\right)}{5\left(x+4\right)\left(x^2+2x+4\right)}=\frac{\left(x-2\right)\left(x^2+2x+4\right)x(x+4)}{5\left(x+4\right)\left(x^2+2x+4\right)}=\frac{x\left(x-2\right)}{5}$.