Assignment:
If F is a field, prove that the field of fractions of F[[x]] is the ring F((x)) of formal Laurent series. Show that the field of fractions of the power series ring Z[[x]] is properly contained in the field of Laurent series Q((x)).
Here F[[x]] is the ring of formal power series in the indeterminate x with coefficients in F.
Provide complete and step by step solution for the question and show calculations and use formulas.