1. ## 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...

2. Originally Posted by nnaiaia
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 $\frac{5x^2+4x+1}{x^2} = \frac{5x^2}{x^2} + \frac{4x}{x^2} + \frac{1}{x^2}$

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