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8.6: Rational Expressions- Answers to the Homework Exercises

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    Reduce Rational Expressions

    1. \(3\)
    1. \(\dfrac{1}{2}\)
    1. undefined; \(a=-1\) is an excluded value
    1. \(-10\)
    1. \(0\)
    1. \(-8,4\)
    1. \(0,-10\)
    1. \(0,-\dfrac{1}{2}\)
    1. \(\dfrac{3}{5a}\)
    1. \(\dfrac{3m-4}{10}\)
    1. \(\dfrac{1}{x+7}\)
    1. \(\dfrac{n+6}{n-5}\)
    1. \(\dfrac{2x-7}{5x-7}\)
    1. \(\dfrac{2n-1}{9}\)
    1. \(\dfrac{9x}{2}\)
    1. \(\dfrac{1}{9}\)
    1. \(\dfrac{7r+8}{8r}\)
    1. \(\dfrac{3(x-3)}{5x+4}\)
    1. \(\dfrac{9}{p+2}\)
    1. \(\dfrac{2(m+2)}{5m-3}\)
    1. \(\dfrac{7n-4}{4}\)
    1. \(\dfrac{7a+9}{2(3a-2)}\)
    1. \(\dfrac{5b-8}{5b+2}\)
    1. \(\dfrac{7x-6}{(3x+4)(x+1)}\)

    Multiply and Divide Rational Expressions

    1. \(4x^2\)
    1. \(\dfrac{3x^2}{2}\)
    1. \(\dfrac{r-6}{r+10}\)
    1. \(\dfrac{x-10}{7}\)
    1. \(5\)
    1. \(\dfrac{4(m-5)}{5m^2}\)
    1. \(\dfrac{b+2}{8b}\)
    1. \(\dfrac{1}{a+7}\)
    1. \(9m^2(m+10)\)
    1. \(\dfrac{5b}{b+5}\)
    1. \(\dfrac{14}{3}\)
    1. \(\dfrac{5p}{2}\)
    1. \(x+4\)
    1. \(\dfrac{1}{v-10}\)
    1. \(\dfrac{p-10}{p-4}\)
    1. \(7\)
    1. \(\dfrac{v-9}{5}\)
    1. \(\dfrac{7}{8(k+3)}\)
    1. \(\dfrac{10}{9(n+6)}\)
    1. \(n+3\)
    1. \(\dfrac{3}{2}\)
    1. \(\dfrac{1}{a+2b}\)
    1. \(\dfrac{x-3}{5x+2}\)
    1. \(\dfrac{x+1}{3x+2}\)

    Obtain the Lowest Common Denominator

    1. \(18\)
    1. \(6a^2c^3\)
    1. \(x^2-x-12\)
    1. \(20xy\)
    1. \(x^2-2x-3\)
    1. \(12a^4b^5\)
    1. \((x+2)(x-4)\)
    1. \((x+1)(x+2)(x+3)\)
    1. \(4(x-2)\)
    1. \((x-3)^2(x+3)\)
    1. \(\dfrac{6a^4}{10a^3b^2},\:\dfrac{2b}{10a^3b^2}\)
    1. \(\dfrac{x^2-4x}{(x-4)^2(x+4)},\:\dfrac{3x^2+12x}{(x-4)^2(x+4)}\)
    1. \(\dfrac{4x}{(x-3)(x+2)},\:\dfrac{x^2+4x+4}{(x-3)(x+2)}\)
    1. \(\dfrac{5}{x(x-6)},\:\dfrac{2x-12}{x(x-6)},\:\dfrac{-3x}{x(x-6)}\)
    1. \(\dfrac{3x^2+4x+1}{(x-4)(x+3)(x+1)},\:\dfrac{2x^2-8x}{(x-4)(x+3)(x+1)}\)

    Add and Subtract Rational Expressions

    1. \(\dfrac{6}{a+3}\)
    1. \(\dfrac{x+6}{x-5}\)
    1. \(\dfrac{15t+16}{18t^3}\)
    1. \(\dfrac{-7x-13}{4x}\)
    1. \(\dfrac{-z^2+5z}{z^2-1}\)
    1. \(\dfrac{4t-5}{4(t-3)}\)
    1. \(\dfrac{t^2+2ty-y^2}{y^2-t^2}\)
    1. \(\dfrac{x-8}{(x+8)(x+6)}\)
    1. \(\dfrac{2x+4}{x^2+4x+3}\)
    1. \(\dfrac{a-2}{a^2-9}\)
    1. \(\dfrac{5(x-1)}{(x+1)(x+3)}\)
    1. \(x-4\)
    1. \(\dfrac{3x+4}{x^2}\)
    1. \(\dfrac{5x+9}{24}\)
    1. \(\dfrac{-c^2+cd-d^2}{c^2d^2}\)
    1. \(\dfrac{11x+15}{4x(x+5)}\)
    1. \(\dfrac{2x+10}{(x+3)^2}\)
    1. \(\dfrac{2x^2-10x+25}{x(x-5)}\)
    1. \(\dfrac{2x-5}{(x-3)(x-2)}\)
    1. \(\dfrac{2x+7}{x^2+5x+6}\)
    1. \(\dfrac{2}{y^2-y}\)
    1. \(\dfrac{5x+5}{x^2+2x-15}\)
    1. \(\dfrac{x+1}{x+2}\)
    1. \(\dfrac{x-4}{x+2}\)

    Compound Rational Expressions

    1. \(\dfrac{x}{x-1}\)
    1. \(-\dfrac{a-1}{a+1}\)
    1. \(-\dfrac{1}{2}\)
    1. \(\dfrac{x}{3}\)
    1. \(\dfrac{x-5}{x+9}\)
    1. \(\dfrac{x-2}{x+2}\)
    1. \(\dfrac{5-a}{a}\)
    1. \(\dfrac{4}{5}\)
    1. \(\dfrac{2a^2-3a+3}{-4a^2-2a}\)
    1. \(\dfrac{x+2}{x-1}\)
    1. \(\dfrac{1}{x+4}\)
    1. \(\dfrac{x-3}{x+4}\)
    1. \(\dfrac{a-3b}{a+3b}\)
    1. \(\dfrac{-2a-2}{3a-4}\)
    1. \(-\dfrac{2x}{x^2+1}\)

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