Solving Equations Containing Rational Expressions

To solve an equation that contains rational expressions, we usually start by clearing the fractions. To do this, multiply each side of the equation by the LCD of all the fractions.

Procedure

To Solve a Rational Equation

Step 1 Find the LCD of the fractions in the equation.

Step 2 Multiply both sides of the equation by the LCD.

Step 3 Use the Distributive Property if necessary.

Step 4 Reduce.

Step 5 Solve the remaining equation.

Step 6 Check the solution.

Example

Solve:

Solution

Step 1 Find the LCD.	LCD = 3 · 2 = 6
Step 2 Multiply by the LCD.
Step 3 Distribute.
Step 4 Reduce.
Step 5 Solve.
Simplify. Subtract 2x from both sides. Subtract 36 from both sides.	2x + 42 42 6	= 3x + 36 = x + 36 = x
Step 6 Check the solution.
So, the solution is x = 6.