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Math Help - Rational equations?

  1. #1
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    Rational equations?

    I am having difficulty solving this equation
    solve the rational equation
    (-4)/(x-1)=7/(2-x)+3/(x+1)
    Please help me.
    So far I got used the least common factor of 2 and (x-1)(x+1)
    To get -8(x+1)=7(x+1)+6(x-1)
    But the answer on the back of my book is 5/13 while I get like -9/21?I am confused.
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  2. #2
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    \displaystyle \frac{-4}{(x-1)}*(x-1)=(x-1)\left[\frac{7}{2-x}+\frac{3}{x+1}\right]\Rightarrow-4=\cdots
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  3. #3
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    Hello, homeylova223!

    \displaystyle \frac{-4}{x-1} \;=\; \frac{7}{2-x} + \frac{3}{x+1}

    I rewrote it like this:

    . . \displaystyle \frac{-4}{x-1} \;=\;\frac{-7}{x-2} + \frac{3}{x+1}


    Then the Least Common Denominator is: . (x-1)(x-2)(x+1)


    Multply through by the LCD:

    . . -7(x-1)(x-2) \;=\; -3(x-1)(x+1) + 3(x-1)(x-2)

    . . . . -4(x^2-x-2) \;=\;-7(x^2-1) + 3(x^2-3x+2)

    . . . . -4x^2 + 4x + 8 \;=\;-7x^2 + 7 + 3x^2 - 9x + 6

    . . . . . . . . . . . . 13x \;=\;5

    . . . . . . . . . . . . . x \;=\;\dfrac{5}{13}

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