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I have the following question: How do they go from step (2) to step (3)? They split a fraction and somehow make $ x^3_n $ into $ \frac{x_n}{3}$ as well and I don't follow ... It's a take on Newtons Method.

This is the equation ...

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    Distribute the negative, break the numerator into parts and simplify the second term. – 2017-02-05

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Isn't it just the fact that $$-\left( \dfrac {a-b}c \right )=-\left(\dfrac ac -\dfrac bc\right) =-\dfrac ac +\dfrac bc$$

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    But where did the power of 3 from $x$ go? Is $x/3$ somehow the same as $x^3/3x^2$ ? ... Yes it is. Thanks ... But how come the negative w turns into a positive one? – 2017-02-05
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    @mathnewbie there are two minus signs in (2) and they cancel out. – 2017-02-05
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    Ah, yeah. I see, thanks. – 2017-02-05
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    Yes, you figured out the power thing. The signs all change because the whole thing is being subtracted. Will add that to answer. – 2017-02-05