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Algebra 2 Rational Equations

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What is the solution set of the equation?
I know the answer is {-1} I just don't know how to get there.

X^2-16 x-3
--------- = ------- -1
(x+4)(x+2) (x+2)

  • Algebra 2 Rational Equations -

    Get a common denominator
    Drop it
    Solve the numerator
    Check your answer- if the answer makes the denominator equal to 0, then drop it (excluded value)

  • Algebra 2 Rational Equations -

    Do not forget 1 needs a common denominator

  • Algebra 2 Rational Equations -

    X-4=x-3-(x+2)
    Common den is x+2
    On the first factor out x+4

  • Algebra 2 Rational Equations -

    (x^2-16)/(x+4)(x+2) - (x-3)/(x+2) + 1 = 0
    place all over a common denominator (x+4)(x+2)

    (x^2-16) - (x-3)(x+2) + (x+4)(x+2)
    ----------------------------------- = 0
    (x+4)(x+2)

    (x^2-16-x^2+x+6+x^2+6x+8)/(x+4)(x+2) = 0

    (x^2+5x+4)/(x+4)(x+2) = 0

    (x+4)(x+1)/(x+4)(x+2) = 0

    (x+1)/(x+2) = 0

    So, f(x) = 0 when x = -1
    Note that the domain excludes x = -4 and -2

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