How to Multiply Rational Expressions? (+FREE Worksheet!)
A rational expression is a ratio of two polynomials and there is a simple way to multiply these expressions, which we will teach you in this article with examples.
Related Topics
- How to Add and Subtract Rational Expressions
- How to Divide Rational Expressions
- How to Solve Rational Equations
- How to Simplify Complex Fractions
- How to Graph Rational Expressions
Method of Multiplying Rational Expressions
- Multiplying rational expressions is the same as multiplying fractions. First, multiply numerators and then multiply denominators. Then, simplify as needed.
Examples
Multiplying Rational Expressions – Example 1:
Solve: x+6x−1×x–15=
Solution:
Multiply numerators and denominators: ab×cd=a×cb×d
x+6x−1×x−15=(x+6)(x−1)5(x−1)
Cancel the common factor: (x−1)
Then: (x+6)(x−1)5(x−1)=(x+6)5
Multiplying Rational Expressions – Example 2:
Solve: x–2x+3×2x+6x–2=
Solution:
Multiply numerators and denominators: x–2x+3×2x+6x–2=(x–2)(2x+6)(x+3)(x−2)
Cancel the common factor: (x−2), then: (x–2)(2x+6)(x+3)(x−2)=(2x+6)(x+3)
Factor 2x+6=2(x+3)
Then: 2(x+3)(x+3)=2
Multiplying Rational Expressions – Example 3:
Solve: x+5x−1×x–13=
Solution:
Multiply fractions: x+5x−1×x–13=(x+5)(x−1)3(x−1)
Cancel the common factor: (x−1),then: (x+5)(x−1)3(x−1)=(x+5)3
Multiplying Rational Expressions – Example 4:
Solve: x–5x+4×2x+8x–5=
Solution:
Multiply fractions: x–5x+4×2x+8x–5=(x–5)(2x+8)(x+4)(x−5)
Cancel the common factor: (x−5), then: (x–5)(2x+8)(x+4)(x−5)=(2x+8)(x+4)
Factor 2x+8=2(x+4)
Then: 2(x+4)(x+4)=2
Exercises for Multiplying Rational Expressions
Multiply Rational Expressions.
- x−4x+3×x+6x–4=
- x+5x+2×xx+5=
- x+9x×x2x+9=
- 3x210×54x=
- x+25x×66x+12=
- x−33x+4×9x+12x−3=
- x+6x+3
- xx+2
- x
- 3x8
- 15x
- 3
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