Derivative of fraction without quotient rule

[mark1]

The following problem appears in my textbook (before it discusses the quotient or product rule, so those rules cannot be used for the answer):

Find the derivative of the function: $$\frac{x^3-3x^2+4}{x^2}$$

I brought the denominator to the top and multiplied it out to get [tex]{x-3+4x^-2}[/ltex]. I then took the derivative of that to get $${1-0-8x^-3}$$, which can be simplified to $$\frac{-7}{x^3}$$.

However, in the back of my book, the answer is given as $$\frac{x^3-8}{x^3}$$.

Please enlighten me as to where i went wrong.

 

[gnome]

Your arithmetic:
$$1 - \frac{8}{x^3} \neq \frac{-7}{x^3}$$

 

[mark1]

Thanks! For some reason, i did the calculus right but messed up on the algebra.

 

[gnome]

It happens.