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Math Help - Simplification problem

  1. #1
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    Simplification problem

    I'm looking at an example in my book. I have the following equation:
    (5x^2+4x+1)/(x^2)

    My book manages to simplify it to:

    5+(4/x)+(1/x^2)

    How did it do this? I see that x^2 is in the denominator, I understand that it would cancel out 5x^2 and leave us with 5. But I assumed that after that, the equation would look like this:

    (5+4x+1)/1 which equals (5+4x+1)

    Which is incorrect. But I don't see why...
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  2. #2
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    Quote Originally Posted by nnaiaia View Post
    I'm looking at an example in my book. I have the following equation:
    (5x^2+4x+1)/(x^2)

    My book manages to simplify it to:

    5+(4/x)+(1/x^2)

    How did it do this? I see that x^2 is in the denominator, I understand that it would cancel out 5x^2 and leave us with 5. But I assumed that after that, the equation would look like this:

    (5+4x+1)/1 which equals (5+4x+1)

    Which is incorrect. But I don't see why...
    It's because by definition of a fraction, it's EVERYTHING in the numerator being divided by the denominator.

    So \frac{5x^2+4x+1}{x^2} = \frac{5x^2}{x^2} + \frac{4x}{x^2} + \frac{1}{x^2}

     = 5 + \frac{4}{x} + \frac{1}{x^2}.
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