Algebraic Manipulation Question

Factor out x from the numerator of the fraction: $x(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009})$

Now, factor out 2 from the denominator: $2(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009})$

So we have ${x(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009}) \over 2(x + 2x^3 + 3x^5 + \cdot \cdot \cdot + 1005x^{2009})} = \color{brown}\boxed{x \over 2}$