Wow this one definitely tested me and was kind of tedious but I think I figured it out for you! First times each term by the LCD which would be T(m)(n). [tex]( \frac{1}{m} (t)(m)(n)) + ( \frac{1}{n} (t)(m)(n)) = ( \frac{1}{t} (t)(m)(n))[/tex] This cancels out the denominators and gives you a new equation. [tex]t(n) + t(m) = m(n)[/tex] This is where it got a little confusing but I moved the terms with m to one side so that they could be factored out to isolate m. [tex]t(n) = m(n) - t(m)[/tex] Factoring out the m from the two terms gives you this equation. [tex]t(n) = m(n - t)[/tex] There is now only one term still connected to the m variable which can just be divided out. Giving you your final answer. [tex] \frac{t(n)}{n - t} = m[/tex]
