How to Divide Rational Expressions? (+FREE Worksheet!)
Dividing Rational Expressions, divide a Rational Expression by another one, can be complicated. In this blog post, you will learn how to divide rational expressions into a few simple steps.
Related Topics
- How to Add and Subtract Rational Expressions
- How to Multiply Rational Expressions
- How to Solve Rational Equations
- How to Simplify Complex Fractions
- How to Graph Rational Expressions
Method of Dividing Rational Expressions
- To divide rational expression, use the same method we use for dividing fractions. (Keep, Change, Flip)
- Keep the first rational expression, change the division sign to multiplication, and flip the numerator and denominator of the second rational expression. Then, multiply numerators and multiply denominators. Simplify as needed.
Examples
Dividing Rational Expressions – Example 1:
\(\frac{x+2}{3x}÷\frac{x^2+5x+6}{3x^2+3x}\)=
Solution:
Use fractions division rule: \(\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}×\frac{d}{c}=\frac{a×d}{b×c}\)
\(\frac{x+2}{3x}÷\frac{x^2+5x+6}{3x^2+3x}=\frac{x+2}{3x}×\frac{3x^2+3x}{x^2+5x+6}=\frac{(x+2)(3x^2+3x)}{(3x)(x^2+5x+6)}\)
Now, factorize the expressions \(3x^2+3x\) and \((x^2+5x+6)\).
Then: \(3x^2+3x=3x(x+1)\) and \(x^2+5x+6=(x+2)(x+3)\)
Simplify: \(\frac{(x+2)(3x^2+3x)}{(3x)(x^2+5x+6)} =\frac{(x+2)(3x)(x+1)}{(3x)(x+2)(x+3)}\), cancel common factors. Then: \(\frac{(x+2)(3x)(x+1)}{(3x)(x+2)(x+3)}=\frac{x+1}{x+3}\)
Dividing Rational Expressions – Example 2:
\(\frac{5x}{x + 3}÷\frac{x}{2x + 6}\)=
Solution:
Use fractions division rule: \(\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}×\frac{d}{c}=\frac{a×d}{b×c}\).
Then: \(\frac{5x}{x + 3}÷\frac{x}{2x + 6}=\frac{5x}{x + 3}×\frac{2x + 6}{x}=\frac{5x(2x + 6)}{x(x+3)}\)
Now, factorize the expressions \(2x+6\), then: \(2(x+3)\)
Simplify: \(\frac{5x(2x + 6)}{x(x+3)}\) =\(\frac{5x×2(x+3)}{x(x+3)}\)
Cancel common factor: \(\frac{5x×2(x+3)}{x(x+3)}=\frac{10x(x+3)}{x(x+3)}=10\)
Dividing Rational Expressions – Example 3:
\(\frac{2x}{5}÷\frac{8}{7}=\)
Solution:
\(\frac{2x}{5}÷\frac{8}{7}=\frac{\frac{2x}{5}}{\frac{8}{7}}\) , Use Divide fractions rules: \(\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a . d}{b . c}\)
\(\frac{\frac{2x}{5}}{\frac{8}{7}}=\frac{(2x)×7}{8×5}=\frac{14x}{40}=\frac{7x}{20}\)
Dividing Rational Expressions – Example 4:
\(\frac{6x}{x + 2}÷\frac{x}{6x + 12}\)=
Solution:
\(\frac{\frac{6x}{x + 2}}{\frac{x}{6x + 12}}\) , Use Divide fractions rules: \(\frac{(6x)(6x+12)}{(x)(x+2)}\)
Now, factorize the expressions \(6x+12\), then: \(6(x+2)\)
Simplify: \(\frac{(6x)(6x+12)}{(x)(x+2)}\) = \(\frac{(6x) × 6(x+2)}{(x)(x+2)}\)
Cancel common fraction: \(\frac{(6x) × 6(x+2)}{(x)(x+2) }\) \(=\frac{36(x+2)}{(x+2)}=36\)
Exercises for Dividing Rational Expressions
Divide Rational Expressions.
- \(\color{blue}{\frac{2x}{7}÷\frac{4}{3}=}\)
- \(\color{blue}{\frac{3}{5x}÷\frac{9}{2x}=}\)
- \(\color{blue}{\frac{7x}{x+6}÷\frac{2}{x+6}=}\)
- \(\color{blue}{\frac{20x^2}{x-1}÷\frac{4x}{x+2}=}\)
- \(\color{blue}{\frac{2x-3}{x+4}÷\frac{5}{6x+24}=}\)
- \(\color{blue}{\frac{x+5}{4}÷\frac{x^2-25}{8}=}\)
- \(\color{blue}{\frac{3x}{14}}\)
- \(\color{blue}{\frac{2}{15}}\)
- \(\color{blue}{\frac{7x}{2}}\)
- \(\color{blue}{\frac{5x(x+2)}{x-1}}\)
- \(\color{blue}{\frac{6(2x-3)}{5}}\)
- \(\color{blue}{\frac{2}{x-5}}\)
The Absolute Best Book for the Algebra Test
Related to This Article
More math articles
- Addition of 3-Digit Numbers
- How to Calculate the Volume of a Truncated Cone: Step-by-Step Guide
- How to Find Standard Deviation
- 10 Most Common 3rd Grade Common Core Math Questions
- How to Navigate the Fraction Jungle: A Guide to Adding Fractions with Unlike Denominators
- How to Use Area Models to Divide Two-Digit Numbers By One-digit Numbers
- How to Solve Inverse Variation?
- Vector-Valued Functions: Fundamentals and Applications
- 10 Most Common 6th Grade MCAS Math Questions
- SAT Math Vs. High School Math
What people say about "How to Divide Rational Expressions? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.