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Math Help - Solve Equation Algebraically

  1. #1
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    Solve Equation Algebraically

    Solve Equation Algebraically not by graphing. What I did was LCD and cross multiply then stuck.
    2/x+2 +3/x-1= -8/5

    answer in solution set should be {-4,-1/8}
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Solve Equation Algebraically

    I assume you meant to type:

    2/(x+2) + 3/(x-1) = -8/5

    Combining terms on the left is a good first step:

    \frac{2(x-1)+3(x+2)}{(x+2)(x-1)}=-\frac{8}{5}

    \frac{5x+4}{(x+2)(x-1)}=-\frac{8}{5}

    Cross-multiplying is a good second step:

    5(5x+4)=-8(x+2)(x-1)

    Now, distributing, we will find a quadratic in x:

    25x+20=-8(x^2+x-2)

    25x+20=-8x^2-8x+16

    Arrange in standard form:

    8x^2+33x+4=0

    Now can you factor this? We see that we need two factors of 32 whose sum is 33...
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