Solving Equations with Fractions
After studying this lesson, you will be able to:
 Solve equations containing fractions.
To Solve Equations containing fractions:
Clear out the fractions by multiplying the ENTIRE equation by
the common denominator.
SPECIAL CASES
Sometimes when dealing with equations, all the variable cancel
out. When this happens we have a "special case". If the
expression we're left with is a true mathematical statement, our
solution is called the Identity Property which
means that there is an infinite number of solutions. The symbol
for infinity is . If the expression we're left with is a false
mathematical statement, there will be no solution. We indicate
this with the empty set symbol which is Ã˜.
Example 1
2x + 5 = 2x 3 
To solve this equation, we need to
attempt to get the variables together on the same side. 
2x + 5  2x = 2x 3  2x 
When we subtract 2x from each side, all
variables are eliminated, leaving us with 5 = 3 
5 = 3 
We know this is a "special
case" since we have no variables. Since 5 is not
equal to 3, this is a false statement. Therefore there
are no solutions. 
Ã˜ 
We write the empty set symbol for our
answer 
Example 2
3 ( x + 1 )  5 = 3x 2 
To solve this equation, we first remove
the parentheses by distributing. 
3x + 3  5 = 3x  2 
We need to collect like terms (3  5 ) on
the left side 
3x  2 = 3x 2 
To solve this equation, we need to
attempt to get the variables together on the same side. 
3x  2  3x = 3x 2  3x 
We do this by subtracting 3x from each
side. This gives us 2 = 2

2 = 2 
We know this is a "special
case" since we have no variables. Since 2 is equal
to 32, this is a true statement (the identity property).
Therefore there are infinite number of solutions. 

We write the symbol for infinity for our
answer 