Section 9.7: Review Exercises

Review the key concepts of rational expressions: simplifying, multiplying/dividing, adding/subtracting, complex fractions, solving equations, and applications.

Simplify Each Expression

  1. \(\dfrac{x^2 - 9}{x^2 - 3x}\)
  2. \(\dfrac{6x^2y}{9xy^2}\)
  3. \(\dfrac{x^2 + 2x + 1}{x^2 - 1}\)

Multiply/Divide Rational Expressions

  1. \(\dfrac{2x}{3} \cdot \dfrac{9}{4x}\)
  2. \(\dfrac{x^2-16}{x+4} \div \dfrac{x-4}{x}\)

Add/Subtract Rational Expressions

  1. \(\dfrac{1}{x} + \dfrac{2}{x+1}\)
  2. \(\dfrac{3}{2x} - \dfrac{1}{4x}\)

Complex Fractions

  1. \(\dfrac{\tfrac{1}{x}+\tfrac{1}{y}}{\tfrac{1}{x}}\)
  2. \(\dfrac{\tfrac{2}{a}}{\tfrac{3}{a}+\tfrac{4}{b}}\)

Solve Rational Equations

  1. \(\dfrac{2}{x} + \dfrac{3}{x+2} = 1\)
  2. \(\dfrac{x}{x+1} = \dfrac{2}{3}\)

Application Problems

  1. If a faucet fills a tank in 5 hours and another in 8 hours, how long together?
  2. A car travels 120 miles downstream in 3 hours and back upstream in 4 hours. Find boat speed in still water and current speed.
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