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Simplifying Complex Fractions That Contain Addition or Subtraction

You have already simplified some complex fractions. Now we will learn how to simplify a complex fraction that contains addition or subtraction.

One way to begin is to carry out the addition or subtraction.

 

Procedure — To Simplify a Complex Fraction That Contains Addition or Subtraction.

Step 1 Perform any addition or subtraction.

Step 2 Rewrite the complex fraction using a division symbol, ÷.

Step 3 Invert the second fraction and change the division symbol, ÷, to the multiplication symbol, ·.

Step 4 Factor the numerators and denominators.

Step 5 Cancel all pairs of factors common to the numerators and denominators.

Step 6 Multiply the numerators. Multiply the denominators.

 

Example 1

Simplify:

Solution

Step 1 Perform any addition or subtraction.  
In both the numerator and denominator the LCD of the fractions is wy.

We write each fraction with LCD.

Then we add the fractions in the numerator and subtract the fractions in the denominator.
Step 2 Rewrite the complex fraction using a division symbol, ÷.
Step 3 Invert the second fraction and change the division symbol, ÷, to the multiplication symbol, ·.
Step 4 Factor the numerators and denominators.
Step 5 Cancel all pairs of factors common to the numerators and denominators.  
The common factors are 2, w, and y.
Step 6 Multiply the numerators. Multiply the denominators.

Thus,

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