# Solve and Graph Rational Equations

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A series of free, online Intermediate Algebra Lessons or Algebra II lessons.
Examples, solutions, videos, worksheets, and activities to help Algebra students.
In this lesson, we will learn

• how to solve rational equations
• how to graph rational functions
• how to solve a rational equation for a parameter or variable

The following figure shows how to solve rational equations. Scroll down the page for more examples and solutions. ### Solving Rational Equations

Solving rational equations is substantially easier with like denominators. When solving rational equations, first multiply every term in the equation by the common denominator so the equation is “cleared” of fractions. Next, use an appropriate technique for solving for the variable.
This video explains how to solve rational equations.

How to solve rational equations.

Examples of how to solve rational equations.

Examples of how to solve rational equations.

### Graphing Rational Functions

The graph of a basic rational function (1/x) is easy to do by plotting key points. When graphing rational functions, the functions are asymptotic to either the x-axis and y-axis or to certain lines if there are shifts in the graphs. More complex graphs of rational functions include functions with graph shifts.

Graphing a Rational Function - Example 1

Graphing a Rational Function - Example 2

Graphing a Rational Function - Example 3

Graphing a Rational Function - Example 4

### Solving a Rational Equation for a parameter

Solving rational equations is substantially easier with like denominators. When solving equations with rational numbers, we first multiply every term in the equation by the common denominator so the equation is “cleared” of fractions. Next, we use an appropriate technique for solving for the variable, such as isolating and simplifying.
How to solve a simple rational equation for a parameter.

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. 