Table of Contents |
Reviewing how to add and subtract numeric fractions is helpful when learning how to add and subtract algebraic fractions. This is because the same general principle is applied in both cases. In order to add two fractions, we want to express each fraction such that the denominators are the same. Then we can simply add or subtract across the numerators and retain the common denominator.
EXAMPLE
When adding , this is fairly straightforward. The denominators are already equivalent, so we can just add the numerators 5 and 3 to get a sum of .When the denominators are not the same, we need to write equivalent equations with the same denominator.
EXAMPLE
Consider the subtraction problem .Multiply by | |
Evaluate multiplication | |
Subtract numerators | |
Evaluate numerator | |
Simplify | |
Our solution |
When the denominators between two factions are the same, adding and subtracting is much easier. This is also the case with rational expressions. Below is an example of adding rational expressions with the same denominator:
EXAMPLE
Add .Add numerators, keep denominator | |
Evaluate numerator | |
Our solution |
When adding or subtracting rational expressions without a common denominator, we must re-express the fractions so that they do have a common denominator. That way, we can add or subtract as we did in the example above.
The easiest way to find a common denominator between two algebraic fractions is to follow these steps:
EXAMPLE
Subtact .Multiply by a fraction made from the denominator of the second fraction, | |
Multiply numerators together by FOILing; denominator is product of the two denominators | |
Combine like terms | |
Our new first fraction |
Multiply by a fraction made from the denominator of the first fraction, | |
Multiply numerators together; denominator is product of the two denominators | |
Our new second fraction |
Replace fractions with results from above | |
Subtract numerators; denominator stays the same | |
Evaluate numerator | |
Combine like terms | |
Our solution |
EXAMPLE
Add .Multiply each fraction by a fraction made up with the denominator of the other | |
Evaluate the multiplication in each numerator | |
Add numerators; denominator stays the same | |
Combine like terms | |
Simplify numerator by factoring out common term, x | |
Cancel x from both numerator and denominator | |
Our solution |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License