Question

Can someone help me out with this? I've used a calculator but none of the answers are options. Also, if you can show work, that would be fantastic.

Answer 1

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).
$( \frac{1}{m} (t)(m)(n)) + ( \frac{1}{n} (t)(m)(n)) = ( \frac{1}{t} (t)(m)(n))$
This cancels out the denominators and gives you a new equation.
$t(n) + t(m) = m(n)$
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.
$t(n) = m(n) - t(m)$
Factoring out the m from the two terms gives you this equation.
$t(n) = m(n - t)$
There is now only one term still connected to the m variable which can just be divided out. Giving you your final answer.
$\frac{t(n)}{n - t} = m$

Hope this helped and was clear enough!
:)