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Math Help - Rational expressions. Solve equations.

  1. #1
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    Rational expressions. Solve equations.

    Please help me with my homework, I've been solving it from 4 hours and everything is wrong. I just cant get the same answer that the back of the book has.

    1. Solve equations.
    a)

    \frac{x}{3-x}+ 3=\frac{5}{2x-6}
    b)

    \frac{4}{2x^2+x}- \frac{6x}{2x+1}= 1

    2.transform to canonical form
    f(x)=\frac{x+3}{x+2}

    f(x)=\frac{2x}{x-1}
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  2. #2
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    Re: Rational expressions. Solve equations.

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

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

    get a common denominator ...

    \frac{-2x}{2(x-3)} + \frac{3 \cdot 2(x-3)}{2(x-3)} = \frac{5}{2(x-3)} ... note that x \ne 3 (why?)

    all denominators are common, the numerators form the equation

    -2x + 6(x-3) = 5

    finish it.
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