unlocking an algebraic expression

An example of an algebraic expression that is ‘locked’ is a binomial in the denominator. Specifically, for x near 0, the locked expression ‘1 + x’ in the larger expression 1/(1 + x) can be unlocked, for many practical purposes, by replacing the entire larger expression by 1 – x. An example of this maneuver is in deriving the formula for how specific mass depends on temperature.
Here is the link to a derivation of this formula. (It is equation #7.)
keywords: Mathematics, Thermodynamics