Solving Equations with Fractions

 The use of the LCD in solving equations with fractions is expanded to include fractions with rational denominators.  To solve an equation that contains fractional terms: 1) determine the LCD, 2) multiply all terms of the equation by the LCD this results in an equation with no fractions, 3) solve the equation, and 4) check the solution in the equation and reject any solution that causes the denominator to become zero.

Example 1:              

                           determine the LCD by factoring the denominators

                                            LCD [(p+3), 8, 4(p+3)] = 8(p+3)

                       multiply all terms by LCD

                                          the result is an equation with no fractions

                                                  distribute and solve equation

                                                  since p = 3 would be the only answer that would cause
                                                               the denominator to equal zero, p = 5 should be correct

Example 2:   
                                  determine the LCD by factoring the denominators

          LCD = (r+3)(r3), multiply all terms by LCD

                                   the result is an equation with no fractions

                                        distribute and solve equation

              

Remember, you must test your solution for validity by substituting r = 3 in the denominator and checking for zeros.  For this problem, when testing your solution the denominator becomes zero; therefore, there is no solution to this equation.
 

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 06-Nov-2007