When the equation you are given has fractions and you prefer not to work with fractions, you can clear the fractions in the first step. Of course, the solution might be a fraction, but that fraction will not occur until the last step. Find the LCD of all fractions and multiply both sides of the equation by this number. Then, distribute this quantity on each side of the equation.
Examples
A common mistake is to fail to distribute the LCD. Another is to multiply only one side of the equation by the LCD.
In the first example, 
, one common mistake is to
multiply both sides by 5 but not to distribute 5 on the left-hand side.
Another common mistake is not to
multiply both sides of the equation by the LCD.
In each case, the last line is not equivalent to the first line—that is, the solution to the last equation is not the solution to the first equation.
In some cases, you will need to use the associative property of multiplication with the LCD instead of the distributive property.
Example
The LCD is
6.
On each side, there are three quantities being multiplied together. On the left, the quantities are 6, ⅓ and x + 4. By the associative law of multiplication, the 6 and ⅓ can be multiplied, then that product is multiplied by x + 4. Similarly, on the right, first multiply 6 and ½, then multiply that product by x – 1.
Practice
Solve for x after
clearing the fraction.
Solutions
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