Skip to main content
Mathematics LibreTexts

1.6E: Rational Expressions (Exercises)

  • Page ID
    56058
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    For the following exercises, simplify the expression.

    61. \(\frac{x^{2}-x-12}{x^{2}-8 x+16}\)
    62. \(\frac{4 y^{2}-25}{4 y^{2}-20 y+25}\)
    63. \(\frac{2 a^{2}-a-3}{2 a^{2}-6 a-8} \cdot \frac{5 a^{2}-19 a-4}{10 a^{2}-13 a-3}\)
    64. \(\frac{d-4}{d^{2}-9} \cdot \frac{d-3}{d^{2}-16}\)
    65. \(\frac{m^{2}+5 m+6}{2 m^{2}-5 m-3} \div \frac{2 m^{2}+3 m-9}{4 m^{2}-4 m-3}\)
    66. \(\frac{4 d^{2}-7 d-2}{6 d^{2}-17 d+10} \div \frac{8 d^{2}+6 d+1}{6 d^{2}+7 d-10}\)
    67. \(\frac{10}{x}+\frac{6}{y}\)
    68. \(\frac{12}{a^{2}+2 a+1}-\frac{3}{a^{2}-1}\)
    69. \(\frac{\frac{1}{d}+\frac{2}{c}}{\frac{6 c+12 d}{d c}}\)
    70. \(\frac{\frac{3}{x}-\frac{7}{y}}{\frac{2}{x}}\)

    This page titled 1.6E: Rational Expressions (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

    • Was this article helpful?