# Solve Rational Equations

Common Core: HSA-REI.A.2

Related Topics:
Algebra Word Problems
Common Core (Algebra)
Common Core for Mathematics

Examples, solutions, videos and lessons to help High School students learn how to solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

### Suggested Learning Targets

• Solve simple rational and radical equations in one variable and provide examples of how extraneous solutions arise.
The following figure shows how to solve rational equations. Scroll down the page for more examples and solutions.

Extraneous Solutions to Rational Equations
Examples:
Solve and eliminate any extraneous solutions:
x2/(x + 2) = 4/(x + 2)
Solve a Rational Equation with Extraneous Solution
Solve a rational equation by multiplying both sides by the LCD and check the answers for extraneous solutions.
Solve 4(x - 3)/(x2 - 36) = 1/(6 - x) + 2x/(6 + x)

Solving Rational Equations
This video explains how to solve rational equations.
Examples:
1. 2/3 - 5/6 = 1/t
2. (x + 2)/(x - 6) = (x - 1)/(x + 2)
3. x/(x + 3) - x/(x - 2) = 10/(x2 + x - 6)
4. 4y/(y + 2) - 3y/(y - 1) = (y2 - 8y - 4)/(y2 + y - 2) Ex 1: Solving Rational Equations.
Examples:
1. 2x/15 - 1/6 = x/5
2. 5/(x - 3) = 4/(x + 2)
Ex 2: Solving Rational Equations.
Examples:
1. 2/5x - 3 = 4/x
2. 2x - 16/x = 4
Ex 3: Solving Rational Equations.
Examples:
1. (x + 4)/x = 6/(x - 4)
2. 5/(x - 7) = -2x/(x + 3)
Ex 4: Solving Rational Equations.
Examples:
1. x/(x - 2) - x/(x2 - 4) = (x + 3)/(x + 2)
2. 5/(x - 3) = 4/(x + 2)
Ex 5: Solving Rational Equations.
Examples:
1. (x - 3)/(x + 6) + (x - 2)/(x - 3) = x2/(x2 + 3x - 18)
2. 5/(x - 3) = 4/(x + 2)

Applications of Rational Equations I
The video explains application problems that use rational equations. Part 1 of 2. Applications of Rational Equations II
The video explains application problems that use rational equations. Part 2 of 2.

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