Rational Equations
A free Algebra II lesson from the “Equations, Rational Functions, and Conics” unit, with a worked example and practice problems including step-by-step solutions.
Rational equations contain fractions with variables. Multiply by the least common denominator to clear fractions, then solve and check that no denominator becomes zero.
What you'll learn
- Solve rational equations
- Clear denominators
- Check for extraneous solutions
Worked example
Problem. Solve x/3 = 5.
- Multiply both sides by 3.
- x = 15.
- Check: 15/3 = 5.
Answer: 15
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Solve x/4 = 7.
Show solution
- Multiply by 4.
Answer: 28
2. Solve 3/x = 1 when x is not 0.
Show solution
- 3/x = 1 means x = 3.
Answer: 3
3. Solve x/5 + 2 = 8.
Show solution
- Subtract 2.
- x/5 = 6.
Answer: 30
4. Solve 12/(x - 1) = 3.
Show solution
- Multiply by x - 1.
- 12 = 3(x - 1).
Answer: 5
5. Why must rational equation solutions be checked?
Choices: They can make a denominator zero · They always have two answers · They cannot be graphed · They are never real
Show solution
- Excluded values are not allowed.
Answer: They can make a denominator zero
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