long term rates = average expected short term rates over the same horizon plus a term premium.
In short: LT rates = avg. exp ST rates + TP (3/x)
YC spread = 10 yr - 1 yr = [avg. exp. ST rates(10yr) - avg. exp. ST rates (1yr)] + [TP(10yr) - TP(1yr)].
This decomposition can be used to see why the YC is inverting. (4/x)