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Solve for $m$ in $F=G\Big(\dfrac{mM}{r^2}\Big)$

I ended up with $\frac{F}{G}\frac{r^2}{M}=m.$ Can I simplify it further or did I completely mess up the answer? I got to where I was by dividing both sides by $G$ then multiplying it by $r^2$ and the n dividing by $M$.

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    Your answer is correct. I guess that's it. There are no further simplifications.2012-08-27
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    One thing though, if $G$ was a function, then things would be slightly different. Let $G^{-1}$ denote the inverse of $G$. Then $m = \dfrac{r^2}{M} G^{-1}(F).$2012-08-27

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