How to Add, Subtract and Simplify Rational Expressions  Examples With Detailed Solutions
How to add, subtract and simplify rational expressions? Grade 11 examples are presented along with detailed solutions and more questions with detailed Solutions and explanations are included.
How to add, subtract and simplify rational expressions?
Adding, subtracting and simplifying rational expressions is done in the same way as adding, subtracting and simplifying fractions. Two cases are possible:
case 2: The fractions or rational expressions do not have the same denominator, we first convert to a common denominator then add or subtract. In fractions, integers only are involved while algebraic expressions are involved in rational expressions. If you have difficulties in adding, subtracting and simplifying fractions and rational expressions, this tutorial will help you overcome those difficulties on the condition that you understand every step involved in solving these questions and also spend more time practicing if needed. I will present the examples below starting with fractions first and then with rational expressions, with more challenging questions as you walk through the tutorial. You need to understand each step!
Example 1: Subtract and simplify: .
Example 2: Subtract and simplify: . Solution: The two fractions have different denominators and we therefore need to convert them to the same denominator. We first find the lowest common multiple (LCM) of the two denominators 5 and 10. 5: 5, 10, 15, ... (multiply 5 by 1, 2, 3, ... to obtain a list of multiples of 5) 10: 10, 20, 30, ... (multiply 10 by 1, 2, 3, ... to obtain a list of multiples of 10) The first common multiple (or the lowest, in red in the lists above) will be used as the common denominator which is also called lowest common denominator (LCD). We now convert all denominator to the common denominator 10 as follows: then simplify Example 3: Simplify: . Solution: The three denominators are different and therefore we need to find a common denominator. We first find the lowest common multiple (LCM) of the two denominators 8, 12 and 16. 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80,... 12: 12, 24, 36, 48, 60, 72, 84, 96,... 16: 16, 32, 48, 64, 80, 96... The lowest common denominator is 48 and we now convert all 3 denominators to the common denominator 48 and simplify as follows: Example 4: Subtract and simplify: . Solution: The two rational expressions have the same denominator and therefore we subtract as follows then simplify
Example 5: Write as a rational expression: .
NOTE: For the following examples, you need to know How to Find lowest common multiple (LCM) of Expressions and also practice on questions on detailed solutions on LCM.
Example 6: Add and simplify: .
Example 7: Add and simplify: .
Example 8: Add and simplify: .
Example 9: Subtract and simplify: .
Example 10: Simplify: .
Example 11: Subtract and simplify: .
More Questions: Add, subtract and simplify the following:

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