Subtracting Rational Expressions
More Algebra Lessons
A rational expression is a fraction in which either the numerator, or the denominator, or both the numerator and the denominator are algebraic expressions.
In this lesson, we will be looking at how to subtract rational expressions with the same denominator and rational expressions with different denominators.
Subtracting Rational Expressions with Same Denominators
When the denominators of two algebraic fractions are the same, we can subtract the numerators and then simplify when possible.
Example:
Simplify the following expression:
Solution:
How to subtract rational expressions with same denominators?
Example:
(8f - g)/2 - (8f + g)/2
How to add and subtract rational expressions with the the same denominators?
Examples:
1. (4x - 1)/(x - 3) + (1 + 3x)/(x - 3) =
2. (x2 + 7x)/(x - 7) - (10x + 28)/(x - 7) =
Subtracting Rational Expressions with Different Denominators
When the denominators of two algebraic fractions are different, we need to find the Least Common Multiple of the denominators (or LCD) before we subtract the fractions.
Here are the steps you need to follow:
Step 1: Find the LCD
Step 2: Express each fraction with the LCD as the denominator.
Step 3: Subtract the numerators and simplify when possible.
Now we apply the above 3 steps in the following example.
Example:
Express the following as a fraction with a single denominator:
Solution:
How to subtract rational expressions with different denominators?
Example:
(-7f)/(f - n) - (4f - n)/(4f - 4n) =
How to subtract rational expressions with different trinomial denominators?
Example:
(3q + 4)/(3q2 + 5q - 28) - (5q + 3)/(2q2 + 3q - 20) How to add and subtract rational expressions when the denominators are different?
Examples:
3/(x - 3) + 2/(x + 5)
7/(x + 2) - 5/(x + 3)
How to subtract rational expressions with unlike denominators?
(2x + 5)/(x2 + 3x -10) - 3/(x + 6)
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.
