91Ó°ÊÓ

Decide whether each of the following is an expression or an equation. (a) \(\frac{2}{x}=\frac{4}{3 x}+\frac{1}{3}\) (b) \(\frac{4}{3 x}+\frac{1}{3}\) (c) \(\frac{5}{x+1}-\frac{2}{x-1}\) (d) \(\frac{5}{x+1}-\frac{2}{x-1}=\frac{4}{x^{2}-1}\)

Give the domain of each rational function using (a) set-builder notation and (b) interval notation. $$ f(x)=\frac{6 x-5}{7 x+1} $$

As review, add or subtract the rational numbers as indicated. Write answers in lowest terms. $$\frac{5}{18}+\frac{7}{12}$$

Give the domain of each rational function using (a) set-builder notation and (b) interval notation. $$ f(x)=\frac{2 x+4}{3 x^{2}+11 x-42} $$

Give the domain of each rational function using (a) set-builder notation and (b) interval notation. $$ f(x)=\frac{x+2}{14} $$

Give the domain of each rational function using (a) set-builder notation and (b) interval notation. $$ f(x)=\frac{x-9}{26} $$

Solve each equation. $$p+\frac{15}{p}=-8$$

Suppose that the given expressions are denominators of rational expressions. Find the least common denominator (LCD) for each group of denominators. $$18 x^{2} y^{3}, \quad 24 x^{4} y^{5}$$

Use either method to simplify each complex fraction. \(\frac{\frac{y+3}{y}-\frac{4}{y-1}}{\frac{y}{y-1}+\frac{1}{y}}\)

Nurses use proportions to determine the amount of a drug to administer when the dose is measured in milligrams but the drug is packaged in a diluted form in milliliters. (Data from Hoyles, C., R. Noss, and S. Pozzi, "Proportional Reasoning in Nursing Practice," Journal for Research in Mathematics Education.) For example, to find the number of milliliters of fluid needed to administer \(300 \mathrm{mg}\) of a drug that comes packaged as \(120 \mathrm{mg}\) in \(2 \mathrm{~mL}\) of fluid, a nurse sets up the proportion $$\frac{120 \mathrm{mg}}{2 \mathrm{~mL}}=\frac{300 \mathrm{mg}}{x \mathrm{~mL}}$$ where \(x\) represents the amount to administer in milliliters. Use this method to find the correct dose for each prescription. \(120 \mathrm{mg}\) of amikacin packaged as \(100 \mathrm{mg}\) in 2 -mL vials