Question

[Calc 1 / Alg 2] What did they do here?

Answer 1

It would be easier to do this with logarithmic differentiation. That is, take the log, then differentiate. d/dx ln v(x) = v'(x)/v(x).

Answer 2

The numerator in that line is just factored out of the numerators in the previous line.

If you can't follow a factoring step, distributing is easier, so see if you can go backwards to check it.