As the title suggests, why are some algebraic equations displayed as inverses instead of equalling the direct variable we're trying to solve?
For example, consider the d-spacing formulas used in crystallography where the variable of interest is d.
Why not just make all the equations equal to d not 1/d^2? If I want to use the equations I have to rearrange them anyway. is there a visual aspect to the equations I'm not seeing? I've seen a lot of other equations be put in inverse form too but I'm not too sure what the benefit is.
Because the expressions for $1/d^2$ are overall simpler than for $d^2$. While the expressions for $d^2$ would be no different in complexity in the first, fourth, and seventh cases, they would be more complex in the other four cases: either introducing double-decker fractions or longer polynomial expressions if the numerators and denominators are multiplied up to clear the extra layer of fractions.