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Fractional (or Rational) Inequalities

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Examples, solutions, videos, activities and worksheets to help A Level Maths students solve fractional inequalities using three methods:
1. Algebraic Method.
2. Graphical Method.
3. Analytical Method.

What are fractional inequalities?
Fractional inequalities are inequalities that contain fractions and there are functions of x in the denominator.

How to solve fractional inequalities?
When solving fractional inequalities we should only multiply both sides by positive values otherwise we would change the sign of the inequality.

The following videos show how to solve fractional inequalities using the algebraic method, graphical method and analytical method.

Solving Fractional Inequalities (1)
Using the algebraic method
Example:
Solve x - 2 < 3/x
Solving Fractional Inequalities (2)



Solving Fractional Inequalities (3)
Using the algebraic method
Example:
Solve (3 - x)/(x - 8) ≥ 1/x
Solving Fractional Inequalities (4)
Using the graphical method
Example:
Solve (3 - x)/(x - 8) ≥ 1/x
Solving Fractional Inequalities (5)
Using the analytical method
Example:
Solve (3 - x)/(x - 8) ≥ 1/x

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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