91Ó°ÊÓ

Perform the operations and simplify, if possible. a. \(\frac{3 x+6}{4} \cdot \frac{4 x+8}{3} \quad\) b. \(\frac{3 x+6}{4} \div \frac{4 x+8}{3}\)

Perform the operations. Then simplify, if possible. a. \(\frac{x}{9}+\frac{2 x}{9}\) b. \(\frac{x}{9} \cdot \frac{2 x}{9}\) c. \(\frac{x}{9} \div \frac{2 x}{9}\)

Explain how to add two rational expressions with unlike denominators.

Simplify. $$ \frac{\frac{2}{b^{2}-1}-\frac{3}{a b-a}}{\frac{3}{a b-a}-\frac{2}{b^{2}-1}} $$

For each of the following purchases, determine the better buy. 98\. Donuts: A dozen for \(\$ 6.24\) or a baker's dozen ( 13 ) for \(\$ 6.65\)

For each expression, perform the indicated operations and then simplify, if possible. Solve each equation and check the result. $$ \text { a. } \frac{u^{2}+1}{u^{2}-u}-\frac{u}{u-1} $$ $$ \text { b. } \frac{u^{2}+1}{u^{2}-u}-\frac{u}{u-1}=\frac{1}{u} $$

Simplify. If an expression cannot be simplified, write "Does not simplify." $$ \frac{18 c-2 c^{2}}{81 d-9 c d} $$

Perform the operations and simplify, if possible. a. \(\frac{4 a-8}{5} \cdot \frac{5 a-10}{4} \quad\) b. \(\frac{4 a-8}{5} \div \frac{5 a-10}{4}\)

When will the LCD of two rational expressions be the product of the denominators of those rational expressions? Give an example.

Perform the operations. Then simplify, if possible. a. \(\frac{m+6}{5}-\frac{m+2}{5}\) b. \(\frac{m+6}{5} \cdot \frac{m+2}{5}\) c. \(\frac{m+6}{5} \div \frac{m+2}{5}\)