<s>[INST] Simplification - Pre Algebra I have $$\frac{x^4+2x}{x^4}$$ which becomes $$\frac{x^3+2}{x^3}$$ after pulling out the common factor.  I wanted to know why you you don't simplify $\frac{x^4+2x}{x^4}$ to $2x$ and the two $x^4$ cancel each other out, or is this because you must apply the denominator fraction to all numerator parts?  So $\frac{x^4}{x^4}$ and $\frac{2x}{x^4}$ which doesn't work.
 [/INST] You can either do
$$\frac{x^4+2x}{x^4} = \frac{x(x^3+2)}{x(x^3)} = \frac{x^3+2}{x^3}$$
and then split the fraction as
$$\frac{x^3+2}{x^3} = \frac{x^3}{x^3} + \frac{2}{x^3} = 1 + \frac{2}{x^3}$$
Alternatively, split up first, and cancel common factors:
$$\frac{x^4+2x}{x^4} = \frac{x^4}{x^4} + \frac{2x}{x^4} = 1 + \frac{2}{x^3}$$
Either way works, though the second is quicker and a bit more straightforward.
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