Dividing rational expressions

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Introduction

Lessons

  1. \bullet Review: Dividing Monomials
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Examples

Lessons

  1. Simplifying Rational Expressions Involving Division
    State the restrictions on the variables, then simplify.

    81x64y2÷27x232y\large \frac{81x}{64y^2} \div \frac{27x^2}{32y}
    1. Simplifying Rational Expressions Involving both Multiplication and Division
      State the restrictions on the variables, then simplify.
      1. 72x4y28x5z3×y2x3÷15x4y415z4\frac{72x^4y^2}{8x^5z^3} \times \frac{y^2}{x^3} \div \frac{15x^4y^4}{15z^4}
      2. 15x4y418x2z7×5z35x3y÷25x2y50z5 \frac{15x^4y^4}{18x^2z^7} \times \frac{5z^3}{5x^3y} \div \frac{25x^2y}{50z^5}
    2. Dividing Rational Expressions in Factored Form
      State the non-permissible values for x, then simplify:

      (x+2)(x5)(x+4)÷3(x+2)(x+4)(x)\large \frac{(x+2)}{(x-5)(x+4)} \div \frac{3(x+2)}{(x+4)(x)}
      1. Convert Expressions to Factored Form, then Divide
        State the non-permissible values for x, then simplify:

        3x212xx24÷2x38x2x2x6\large \frac{3x^2-12x}{x^2-4} \div \frac{2x^3-8x^2}{x^2-x-6}
        1. Fractions Dividing Fractions
          State the non-permissible values for x, then simplify:

          25x+104x1025x2+10x(2x5)2\large \frac{ \frac{25x+10}{4x-10}}{\frac{25x^2+10x}{(2x-5)^2}}
          1. Performing Addition First, then Division
            Simplify:

            32a+6+44a43a+5\large \frac{\frac{3}{2a+6}+\frac{4}{4a-4}}{\frac{3}{a}+5}

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            Topic Basics
            \bullet multiplication rule: xaxb=xa+bx^a \cdot x^b=x^{a+b}
            \bullet division rule: xaxb=xab\frac{x^a}{x^b}=x^{a-b}