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
- How to Model and Solve Equations Using Algebra Tiles
- TExES Core Math FREE Sample Practice Questions
- Unlock the Future: 10 Unexpected Advantages of Online Learning in 2024
- Remainder and Factor Theorems
- Parallel, Perpendicular, and Intersecting Lines
- Let’s Make Math Education Relevant for Real Life
- 3rd Grade Georgia Milestones Assessment System Math Practice Test Questions
- Reveal the Secrets: “TSI Math for Beginners” Detailed Solution Manual
- How to Find Complementary, Supplementary, Vertical, Adjacent, and Congruent Angles?
- How to Use the Associative and Commutative Properties to Multiply
What people say about "How to Divide Rational Expressions? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.