Solutions

Solutions of Rational Equations

Solving Using LCDs

One way of solving rational equations is to multiply all terms in the equation by the least common denominator (LCD). Then simplify the products, eliminating the denominators.

Example 1 Solve.

Frac1

Step 1. Find the LCD:

12 is the LCD because it is the least common multiple of 12, 3, and 4.

Step 2. Multiply each term by the LCD:

frac2

Frac3

Cancel

Frac5

Step 3. Set the equation equal to zero.

Frac6

Step 4. Solve by factoring and use the Zero Product Property.

Frac7

Frac8 orFrac9

Frac10 or Frac11

*Remember: you can always check your answers by plugging the solutions into the original equation.