Wize High School Algebra I Textbook (Common Core) > Rational Expressions and 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}xy22x3​×6x415y​

=2x3×15yxy2×6x4=\dfrac{2x^3\times15y}{xy^2\times6x^4}=xy2×6x42x3×15y​

=30x3y6x5y2=\dfrac{30x^3y}{6x^5y^2}=6x5y230x3y​

=5x2y=\dfrac{5}{x^2y}=x2y5​

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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}xy22x3​÷6x415y​

=2x3xy2×6x415y=\dfrac{2x^3}{xy^2}\times\dfrac{6x^4}{15y}=xy22x3​×15y6x4​

=2x3×6x4xy2×15y=\dfrac{2x^3\times6x^4}{xy^2\times15y}=xy2×15y2x3×6x4​

=12x715xy3=\dfrac{12x^7}{15xy^3}=15xy312x7​

=4x65y3=\dfrac{4x^6}{5y^3}=5y34x6​

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)}(2x+1)(x+2)x(x+2)2(x−5)​×x(x−5)(x+3)(x+4)​

Enter the simplified expression (to enter a fraction

\dfrac{a}{b}

, type a / b).

Check the solutions to see if you got the restrictions right.

I don't know

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}(x2+4)(x−3)x5−16x​÷2x3−4x2−6xx2−x−2​, and then state all of the restrictions.

Enter the simplified expression (to enter a fraction

\dfrac{a}{b}

, type a / b).

Check the solutions to see if you got the restrictions right.

I don't know

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=2x=2

a) Enter the simplified expression for the area (to enter

\dfrac{a}{b}

, type a/ b)

b) Enter the area of the triangle without units.

I don't know