Solving Equations That Contain Rational
Expressions
Solving an equation that contains rational expressions is like solving an
equation that contains fractions. Let’s begin by solving an equation that
has only integers in the denominators of the rational expressions.
Example
Solve:
Solution
| To clear the fractions, multiply each
side of the equation by the LCD of
all the rational expressions. |
 |
 |
| In this example, the LCD is 12.
|
 |
 |
| Distribute 12 to each term on the left
side.
|
 |
 |
| To reduce, cancel common factors. |
 |
 |
| Simplify.
|
4x - 3 |
= 2x + 1 |
| Subtract 2x from both sides and add
3 to both sides. |
2x |
= 4 |
| Divide both sides by 2. |
x |
= 2 |
The result is x = 2.
To check the solution, substitute 2 for x in
the original equation and simplify.
Check x = 2
|