91Ó°ÊÓ

For the following exercises, perform the indicated operations. $$ \frac{10 m^{2}+80 m}{3 m-9} \cdot \frac{m^{2}+4 m-21}{m^{2}-9 m+20} \div \frac{5 m^{2}+10 m}{2 m-10} $$

For the following exercises, perform the indicated operations. $$ \frac{4 n^{2}+32 n}{3 n+2} \cdot \frac{3 n^{2}-n-2}{n^{2}+n-30} \div \frac{108 n^{2}-24 n}{n+6} $$

For the following exercises, perform the indicated operations. $$ \frac{12 p^{2}+3 p}{p+3} \div \frac{p^{2}+2 p-63}{p^{2}-p-12} \cdot \frac{p-7}{9 p^{3}-9 p^{2}} $$

For the following exercises, perform the indicated operations. $$ \frac{6 q+3}{9 q^{2}-9 q} \div \frac{q^{2}+14 q+33}{q^{2}+4 q-5} \cdot \frac{4 q^{2}+12 q}{12 q+6} $$

In the following exercises, find the domain of each function. $$ R(x)=\frac{x^{3}-2 x^{2}-25 x+50}{x^{2}-25} $$

In the following exercises, find the domain of each function. $$ R(x)=\frac{x^{3}+3 x^{2}-4 x-12}{x^{2}-4} $$

In the following exercises, find the domain of each function. $$ R(x)=\frac{3 x^{2}+15 x}{6 x^{2}+6 x-36} $$

In the following exercises, find the domain of each function. $$ R(x)=\frac{8 x^{2}-32 x}{2 x^{2}-6 x-80} $$

For the following exercises, find \(R(x)=f(x) \cdot g(x)\) where \(f(x)\) and \(g(x)\) are given. $$ \begin{array}{l} f(x)=\frac{6 x^{2}-12 x}{x^{2}+7 x-18} \\ g(x)=\frac{x^{2}-81}{3 x^{2}-27 x} \end{array} $$

For the following exercises, find \(R(x)=f(x) \cdot g(x)\) where \(f(x)\) and \(g(x)\) are given. $$ \begin{array}{l} f(x)=\frac{x^{2}-2 x}{x^{2}+6 x-16} \\ g(x)=\frac{x^{2}-64}{x^{2}-8 x} \end{array} $$