Solutions

Solutions of Rational Equations

Solving Using LCDs

Example 2

Solve.

frac1

Step 1. Factor all denominators.

Frac2

Step 2. Find the LCD.

frac3 is the LCD because it is the least common multiple of the three denominators
{(x + 2),(x – 5), and (x+2)(x-5)}.

Step 3. Multiply all terms in the equation by the LCD.

Cancel

Step 4. Simplify and solve the resulting polynomial equation.

Solution

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