How would I simplify the following equation to solve for $x$?
$$ \frac{\exp(\frac{1-x}{20}) + \exp(\frac{10-x}{20})} {\exp(\frac{1-x}{5}) + \exp(\frac{10-x}{5})} = 4 $$
What about if there were additional terms in each sum, i.e.
$$ \frac{\exp(\frac{1-x}{20}) + \exp(\frac{10-x}{20}) + \exp(\frac{20-x}{20})} {\exp(\frac{1-x}{5}) + \exp(\frac{10-x}{5}) + \exp(\frac{20-x}{5})} = 4 $$
HINT
Note that $$ \exp\left(\frac{1-x}{20}\right) = \frac{e^{1/20}}{e^{x/20}} $$ so the numerator will simplify to expressions involving $e^{x/20}$, and the numerator will be in terms of $e^{x/5}$. Note that if we let $u = e^{x/20}$ then $e^{x/5} = \left(e^{x/20}\right)^4 = u^4$ and now plug in and simplify.