How to Add and Subtract Rational Expressions? (+FREE Worksheet!)

By knowing a few simple rules you can easily add and subtract Rational Expressions. In this blog post, we will introduce you step by step guide on how to add and subtract rational expressions.
Related Topics
- How to Multiply Rational Expressions
- How to Divide Rational Expressions
- How to Solve Rational Equations
- How to Simplify Complex Fractions
- How to Graph Rational Expressions
A step-by-step guide to Adding and Subtracting Rational Expressions
For adding and subtracting rational expressions:
- Find the least common denominator (LCD).
- Write each expression using the LCD.
- Add or subtract the numerators.
- Simplify as needed
Examples
Adding and Subtracting Rational Expressions – Example 1:
Solve: \(\frac{4}{2x+3}+\frac{x-2 }{2x+3}=\)
Solution:
The denominators are equal. Then, use fractions addition rule: \(\frac{a}{c}±\frac{b}{c}=\frac{a ± b}{c}→\frac{4}{2x+3}+\frac{x-2}{2x+3}=\frac{4+(x-2) }{2x+3}=\frac{x+2}{2x+3}\)
Adding and Subtracting Rational Expressions – Example 2:
Solve \(\frac{x + 4}{x – 5}+\frac{x – 4}{x + 6}\)=
Solution:
Find the least common denominator of\( (x-5)\) and \((x+6): (x-5)(x+6) \)
Then: \(\frac{x + 4}{x – 5}+\frac{x – 4}{x + 6}=\frac{(x+4)(x+6)}{(x-5)(x+6)}+\frac{(x – 4)(x-5)}{(x + 6)(x-5)}=\frac{(x+4)(x+6)+(x – 4)(x-5)}{(x + 6)(x-5)}\)
Expand: \((x+4)(x+6)+(x-4)(x-5)=2x^2+x+44\)
Then: \(\frac{(x+4)(x+6)+(x – 4)(x-5)}{(x + 6)(x-5)}=\frac{2x^2+x+44}{(x +6)(x-5)}=\frac{2x^2+x+44}{x^2+x-30}\)
Adding and Subtracting Rational Expressions – Example 3:
Solve: \(\frac{3}{x+4}+\frac{x-2 }{x+4}\)=
Solution:
Use fraction addition rule: \(\frac{a}{c}±\frac{b}{c}=\frac{a ± b}{c}→\frac{3}{x+4}+\frac{x-2}{x+4}=\frac{3+(x-2) }{x+4}=\frac{x+1}{x+4}\)
Adding and Subtracting Rational Expressions – Example 4:
Solve: \(\frac{x + 4}{x – 8}+ \frac{x }{x + 6}\)=
Solution:
Least common denominator of \((x-8)\) and \((x+6): (x-8)(x+6)\)
Then: \(\frac{(x+4)(x+6)}{(x-8)(x+6)}+\frac{x(x-8)}{(x + 6)(x-8)}=\frac{(x+4)(x+6)+x(x-8)}{(x + 6)(x-8)}\)
Expand: \((x+4)(x+6)+x(x-8)=2x^2+2x+24\)
Then: \(\frac{x + 4}{x – 8}+ \frac{x }{x + 6}=\frac{2x^2+2x+24}{(x +6)(x-8)}\)
Exercises for Simplifying Fractions
Add and Subtract Rational Expressions.
- \(\color{blue}{\frac{3}{x+1}-\frac{4x}{x+1}=}\)
- \(\color{blue}{\frac{x+8}{x+1}+\frac{x-9}{x+2}=}\)
- \(\color{blue}{\frac{6x}{x+5}+\frac{x+2}{x+7}=}\)
- \(\color{blue}{\frac{15}{x+6}-\frac{x+1}{x^{2}-36}=}\)
- \(\color{blue}{\frac{x+4}{x+3}-\frac{5x}{x-3}=}\)
- \(\color{blue}{\frac{x+8}{x-4}+\frac{x-5}{x^{2}-16}=}\)

- \(\color{blue}{\frac{3-4x}{x+1}}\)
- \(\color{blue}{\frac{2x^2+2x+7}{(x+1)(x+2)}}\)
- \(\color{blue}{\frac{7x^2+49x+10}{(x+5)(x+7)}}\)
- \(\color{blue}{\frac{14x-91}{(x+6)(x-6)}}\)
- \(\color{blue}{\frac{-4x^2-14x-12}{(x+3)(x-3)}}\)
- \(\color{blue}{\frac{x^2+13x+27}{(x+4)(x-4)}}\)
Related to This Article
More math articles
- How to Find Discontinuities of Rational Functions?
- Number Properties Puzzle – Challenge 19
- Geometry Puzzle – Challenge 74
- Full-Length 6th Grade ACT Aspire Math Practice Test
- 10 Most Common 3rd Grade PARCC Math Questions
- How to Study for a Math Test in 7 Easy Steps
- How to Find Magnitude of Vectors?
- How to Create a Proportion? (+FREE Worksheet!)
- Other Topics Puzzle – Challenge 98
- The Ultimate 7th Grade Scantron Math Course (+FREE Worksheets)
What people say about "How to Add and Subtract Rational Expressions? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.