91Ó°ÊÓ

Add or subtract as indicated. Simplify the result, if possible. $$7+\frac{1}{x-5}$$

Perform the indicated operation or operations. $$\left(\frac{6 y^{2}+31 y+18}{3 y^{2}-20 y+12} \cdot \frac{2 y^{2}-15 y+18}{6 y^{2}+35 y+36}\right) \div \frac{2 y^{2}-13 y+15}{9 y^{2}+15 y+4}$$

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{22 b+15}{12 b^{2}+52 b-9}+\frac{30 b-20}{12 b^{2}+52 b-9}-\frac{4-2 b}{12 b^{2}+52 b-9}$$

Why should restrictions on the variable in a rational equation be listed before you begin solving the equation?

Describe similarities and differences between the procedures needed to solve the following problems: $$ \text { Add: } \frac{2}{x}+\frac{3}{4}, \quad \text { Solve: } \frac{2}{x}+\frac{3}{4}=1 $$

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{2 y}{y-5}-\left(\frac{2}{y-5}+\frac{y-2}{y-5}\right)$$

Perform the indicated operation or operations. $$\frac{3 x^{2}+3 x-60}{2 x-8}+\left(\frac{30 x^{2}}{x^{2}-7 x+10} \cdot \frac{x^{3}+3 x^{2}-10 x}{25 x^{3}}\right)$$

Add or subtract as indicated. Simplify the result, if possible. $$3-\frac{3 y}{y+1}$$

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{4-6 x}{3 x^{2}-2 x}$$

Use the \([\text { GRAPH }]\) or \([\text { TABLE }]\) feature of a graphing utility to determine if the simplification is correct. If the answer is wrong, correct it and then verify your corrected simplification using the graphing utility. \(\frac{x-\frac{1}{2 x+1}}{1-\frac{x}{2 x+1}}=2 x-1\)