I'll send an email with an image that should clear it up a bit. Two different approaches to checking a simplification solution can be summarized as: "eye check" or "numeric validation".

An "eye check" means you review the solution steps and verify that it was correctly simplified - this type of approach is much analogous to reading a letter, but "reading algebraic steps".

In contrast, "numeric validation" means you randomly substitute an unsimplified expression with numbers rather than variables, simplify those values to a numeric answer. Then you use the same variable substitutions and convert the simplified expression into a numeric answer. So long as the simplification was correct (both numeric answers agree with each other) then one can be infer that the process was correct.