Simplify part of an expression produced by resol

Mathematica generates an answer with the help of Solve[] but it is not as simplified as possible. By manually organizing this expression, I know that the parts highlighted in yellow can actually be very simplified. I can not use a function like Together[] because I only want to simplify part of the expression (highlighted in yellow)

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By organizing this manually, I know that the entire expression can be written as follows. Note that the highlighted part can be simplified into a single fraction.

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I would be very grateful if anyone can help me with this targeted simplification of what I have highlighted in yellow! And even better, it would be great if I could get the expression that reproduces exactly what I drifted by hand (which would imply two distinct simplifications?)

I've simplified my code as follows:

rdot = 1/2 epsilon (- (r / Q) + (Fo Sin[[Alpha]]) / (k z))
phidot = (epsilon (- ((H R) / (1 - r ^ 2) ^ (3/2)) - - (3 Fo z ^ 2 Cos[[Alpha]]) / r)) / (6 k z ^ 3)

alphadot = epsilon * sigma - phidot

sol = solve[rdot == 0 && alphadot == 0, {sigma, [Alpha]}]