Simplifying and solving fractional equations

Solving fractional equations

Solving fractional equations 

is very much like 

addition and subtraction of fractions, 

but after the first step, 

GET RID of the denominators  

so that you have 

a denominator-free equation.  

Steps To "get rid" of the denominators:

1.  Choose the common denominator for the equation.

2.  Multiply EVERY TERM in the equation 
by the common denominator.

3.  Reduce each term to form a "denominator free" equation.  

Example 1:

Solve:

5 is the only denominator.

Multiply every term of the equation including the 1 by 5:

So:		becomes		which is	2x + 5 = 13 and  x = 4
Answer:  x = 4

  

Example 2:

Solve:

The common denominator is 15.  Multiply every term by 15:

5•(x) – 3•(2x) = - 7 5x – 6x = - 7  -x = -7, so x = 7

Answer:  x = 7

Example 3:

Solve:

The common denominator is 10.  Multiply every term by 10:

Answer:  x = -64

In this problem, the first numerator (x + 3) has more than one term, so it is necessary to use brackets when multiplying.  

TIP:For problems like this one, use (  ) brackets to WRITE OUT the calculations to avoid careless errors.

Example 4:

Solve:

The common denominator is 2x.  Multiply each term by 2x:

Answer:  x = 5 and x = -2

TIP:     USE  ' CROSS MULTIPLY' TO SOLVE THIS PROBLEM.