Practice Drill: Multiplying Rational Algebraic Expressions

What are the three easy steps in multiplying rational expressions?

• Factor.

  Cancel.

  Multiply the numerators.

  Copy the denominators.

  Simplify.

• Factor the numerators and denominators

  Cancel the common factor.

  Copy and multiply the remaining factors.

  Simplify.

• Multiply the numerator to denominator.

  Simplify, if necessary.

• Multiply the first rational expression to the reciprocal of the second rational expression.

  Factor out the expressions.

  Cancel the common factors.

  Copy and multiply the remaining factors.

  Simplify, if necessary.

What are the pre-requisite skills of Mathematics in multiplying rational expressions?

• Factoring Polynomials

• Multiplying Fractions

• Reciprocating Expressions

• Dividing Rational Expressions

Multiply the two rational expressions and simplify the result:

 $\frac{x^2-4}{x^2-9}\cdot\frac{x-3}{x+2}$  

•  $\frac{x-2}{x+3}$  

•  $\frac{x+2}{x-3}$  

•  $-\frac{2}{3}$  

•  $\frac{x-2}{x-3}$  

Multiply the two rational expressions and simplify the result:

 $\frac{x^2-4x+4}{x^2-5x}\cdot\frac{x}{x^2-2x}$  

•  $\frac{x-2}{x-5x}$  

•  $\frac{x-2}{x^2-5x}$  

•  $\frac{x-2}{x-5}$  

•  $\frac{x-4}{x^2-5x}$  

Multiply the two polynomials and simplify the result:

 $\frac{3x+12}{x-5}\cdot\frac{x^2-25}{x^2+9x+20}$  

(a)  

Multiply the two polynomials and simplify the result:

 $\frac{2x^2-x-6}{x-2}\cdot\frac{2x-3}{4x^2-9}$  

(a)  

Multiply the two polynomials and simplify the result:

 $\frac{x^2-12x+35}{2x-10}\cdot\frac{2x-2}{x-7}$  

(a)  

Multiply the two rational expressions and simplify the result:

 $\frac{x^2}{y}\cdot\frac{3y^3}{2x^3}$  

•  $\frac{3y^2}{2x}$  

•  $\frac{y^2}{2x}$  

•  $\frac{y^2}{x}$  

•  $\frac{3y^2}{x}$  

Multiply the two rational expressions and simplify the result:

 $\frac{x-1}{x-2}\cdot\frac{2}{x+2}$  

•  $\frac{1}{x-2}$  

•  $\frac{x-1}{x^2-2x}$  

•  $\frac{2x-2}{x^2-4}$  

•  $\frac{1}{x}$  

Multiply the two rational expressions and simplify the result:

 $\frac{x^2-5x+6}{x^2-4}\cdot\frac{x^2-3x+2}{x^2-9}$  

•  $\frac{x^2-3x-2}{x^2+5x-6}$  

•  $\frac{x-1}{x^2+5x+6}$  

•  $\frac{x^2+3x-2}{x^2-5x+6}$  

•  $\frac{x^2-3x+2}{x^2+5x+6}$