Addition and Subtraction of Algebraic Fractions with Examples

How to add algebraic fractions?

Adding algebraic fractions and adding number fractions are almost same. When we solve algebraic fractions apply all the algebraic rules in order to add all algebraic functions. The most important thing that we need to find is either the denominators are same or not.

Let’s do an example; x/2 + x/5

First we check denominators, in this example x/2 + x/5 denominators are not same, one fraction have 2 as a denominator while other fraction have 5 as a denominator 5.

Therefore denominators are not same, so it means we conclude that we can’t solve it? yes, we can solve it but later, now our focus on adding and subtracting fractions with same denominators.

Addition and subtraction of algebraic fractions with same denominator

Example: x/5 + 2x/5

First we check the denominators. Are both denominators same? Yes both denominators are same as 5, then we can add the denominators.

Here are steps:

Step 1: It is simple When algebraic fractions have same denominators, we should simply add or subtract the numerators and place over the common denominator.

Step 2: The sum of the fraction is reduced to its lowest form.

Example: 2a/4 + 3a/4

These fractions have same denominators so these are like fractions and a is common.

2a/4 + 3a/4 = 5a/4

Addition and subtraction of algebraic fractions with different denominator

These steps are follows:

Step 1: To add or subtract algebraic fractions, first find the lowest common multiple of the denominators. When apply this number for fractions then it is called the (LCD)lowest common denominator.

Step 2: Change each fraction to an equivalent fraction with the common denominator and then combine each numerator.

Express all fractions in terms of the lowest common denominator. We get the same denominator.

Step 3: Add/subtract the numerators and keep the denominator. So, we get a new fraction.

Step 4: Simplify the fraction if possible.