In this chapter, we are going to look at how to add and subtract algebraic fractions. The processes we follow with algebraic fractions are very similar to the processes we use with fractions that only contain numbers. Let's check it out.

Adding and subtracting algebraic fractions

Do you remember that when we are adding or subtracting fractions, we need to have common denominators? Well the same goes for algebraic fractions. We need to find a common factor between the fractions (remember you can always multiply the denominators together to find a common factor).

However in this chapter, we will only deal with the addition and subtraction of algebraic fractions that already share a common denominator. Later we will extend this to the addition and subtraction of any two or more algebraic fractions. Let's take a look at a few examples below.

Worked Examples

Question 1

Simplify $\frac{8x}{12}+\frac{10x}{12}$8x12+10x12

Question 2

Simplify the following: $\frac{8x-5}{5}+\frac{-5x-2}{5}$8x−55+−5x−25

Question 3

Simplify $\frac{6u+1}{2u-3}-\frac{2u+7}{2u-3}$6u+12u−3−2u+72u−3.

QUESTION 4

Simplify $\frac{40}{9p^2+13p+13}-\frac{5p^2}{9p^2+13p+13}$409p2+13p+13−5p29p2+13p+13. Give your answer in factorised form.

Addition and subtraction of rational expressions I