# Thread: Simplification problem

1. ## Simplification problem

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

My book manages to simplify it to:

$\displaystyle 5+(4/x)+(1/x^2)$

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

$\displaystyle (5+4x+1)/1$ which equals $\displaystyle (5+4x+1)$

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:
$\displaystyle (5x^2+4x+1)/(x^2)$

My book manages to simplify it to:

$\displaystyle 5+(4/x)+(1/x^2)$

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

$\displaystyle (5+4x+1)/1$ which equals $\displaystyle (5+4x+1)$

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

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