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How to Multiply Rational Expressions? (+FREE Worksheet!)

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.

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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+6x1×x15=

Solution:

Multiply numerators and denominators: ab×cd=a×cb×d
x+6x1×x15=(x+6)(x1)5(x1)
Cancel the common factor: (x1)
Then: (x+6)(x1)5(x1)=(x+6)5

Multiplying Rational Expressions – Example 2:

Solve: x2x+3×2x+6x2=

Solution:

Multiply numerators and denominators: x2x+3×2x+6x2=(x2)(2x+6)(x+3)(x2)
Cancel the common factor: (x2), then: (x2)(2x+6)(x+3)(x2)=(2x+6)(x+3)
Factor 2x+6=2(x+3)
Then: 2(x+3)(x+3)=2

Multiplying Rational Expressions – Example 3:

Solve: x+5x1×x13=

Solution:

Multiply fractions: x+5x1×x13=(x+5)(x1)3(x1)
Cancel the common factor: (x1),then: (x+5)(x1)3(x1)=(x+5)3

Multiplying Rational Expressions – Example 4:

Solve: x5x+4×2x+8x5=

Solution:

Multiply fractions: x5x+4×2x+8x5=(x5)(2x+8)(x+4)(x5)
Cancel the common factor: (x5), then: (x5)(2x+8)(x+4)(x5)=(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.

  1. x4x+3×x+6x4=
  2. x+5x+2×xx+5=
  3. x+9x×x2x+9=
  4. 3x210×54x=
  5. x+25x×66x+12=
  6. x33x+4×9x+12x3=
This image has an empty alt attribute; its file name is answers.png
  1. x+6x+3
  2. xx+2
  3. x
  4. 3x8
  5. 15x
  6. 3

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