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**1. Homework Statement**

[tex] \frac{d}{dx} [ arctan (2x-3) ] [/tex]

**3. The Attempt at a Solution**

The general solution for d/dx arctan(x) = [tex] \frac{du/dx}{1+x^2} [/tex]

so

[tex] \frac{du/dx}{1+(2x-3)^2} [/tex]

[tex] du/dx = 2 [/tex]

[tex] \frac{2}{1+(2x-3)^2} [/tex]

[tex] \frac{2}{1+2x^2-12x+9} [/tex]

[tex] \frac{2}{10+2x^2-12x} [/tex]

now this is where my question comes in,

When I simplify it, I would divide all the terms in the numerator and denominator by 2,

giving me [tex] \frac{1}{5+x^2-6x} [/tex]

however i've been told that this simplification is wrong without any explanation

why?

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