\(a,\frac{4x}{25y^3}.\frac{2y^2}{x^2}=\frac{4x.2y^2}{25y^3.x^2}=\frac{4.2}{25y.x}=\frac{8}{25xy}\)
\(b,\frac{9a^2}{a+3}.\frac{a^2-9}{6a^3}=\frac{9a^2\left(a-3\right)\left(a+3\right)}{\left(a+3\right).6a^3}=\frac{3\left(a-3\right)}{2a}=\frac{3a-9}{2a}\)
\(c,\frac{4n^2}{17m^4}.\left(-\frac{7m^2}{12m}\right)=\frac{4n^2.\left(-7m^2\right)}{17m^4.12m}=\frac{n.\left(-7\right)}{17m^2.3}=\frac{-7n}{51m^2}\)
\(d,\frac{3b+6}{\left(b-9\right)^2}.\frac{2b-18}{\left(b+2\right)^2}=\frac{3\left(b+2\right).2\left(b-9\right)}{\left(b-9\right)^2.\left(b+2\right)^2}=\frac{3.2}{\left(b-9\right)\left(b+2\right)}=\frac{6}{\left(b-9\right)\left(b+2\right)}\)
\(e,\frac{x+3}{x}.\frac{x^2y}{x^2+6x+9}=\frac{\left(x+3\right).x^2y}{x.\left(x^2+6x+9\right)}=\frac{\left(x+3\right).x^2y}{x.\left(x+3\right)^2}=\frac{xy}{x+3}\)
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