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Wize High School Algebra II Textbook (Common Core) > Rational Functions

Multiplying and Dividing Rational Expressions

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Multiplying & Dividing Rational Expressions

Rational expressions are quotients of polynomials, and they look like fractions. So, we can multiply and divide rational expressions the same way we multiply and divide fractions!

Multiplying Rational Expressions

We multiply the numerators together, and muliply the denominators together, then simplify.
Example
Simplify 2x3xy2×15y6x4\dfrac{2x^3}{xy^2}\times \dfrac{15y}{6x^4}

=2x3×15yxy2×6x4=\dfrac{2x^3\times15y}{xy^2\times6x^4}

=30x3y6x5y2=\dfrac{30x^3y}{6x^5y^2}

=5x2y=\dfrac{5}{x^2y}

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Dividing Rational Expressions

We multiply by the reciprocal of the second rational expression.
Example
Simplify 2x3xy2÷15y6x4\dfrac{2x^3}{xy^2}\div\dfrac{15y}{6x^4}

=2x3xy2×6x415y=\dfrac{2x^3}{xy^2}\times\dfrac{6x^4}{15y}

=2x3×6x4xy2×15y=\dfrac{2x^3\times6x^4}{xy^2\times15y}

=12x715xy3=\dfrac{12x^7}{15xy^3}

=4x65y3=\dfrac{4x^6}{5y^3}

Practice: Multiplying & Dividing Rational Expressions

Simplify the expression, then state any restrictions.

x(x+2)2(x−5)(2x+1)(x+2)×(x+4)x(x−5)(x+3)\dfrac{x(x+2)^2(x-5)}{(2x+1)(x+2)}\times\dfrac{(x+4)}{x(x-5)(x+3)}

Practice: Multiplying & Dividing Rational Expressions

Simplify the expression x5−16x(x2+4)(x−3)÷x2−x−22x3−4x2−6x\dfrac{x^5-16x}{(x^2+4)(x-3)}\div\dfrac{x^2-x-2}{2x^3-4x^2-6x}, and then state all of the restrictions.

Practice: Multiplying & Dividing Rational Expressions


a) Find a simplified expression that represents the area of the triangle. State all of the restrictions

b) Find the area of the triangle if x=2x=2