The goal is to get m alone on one side of the equals and to get things not m on the other. With two m terms on the left it looks fine, but subtracting one sends it to the other side. Adding it back takes us back to the start.
That's not the way to start. Instead, m and s are put together with multiplying. So are m and t. Let's try instead to get m away from the other variables.
ms + mv = t
m (s + v) = t <--- factor m out as a common factor
m = t / (s + v) < ---- divide both sides by s + v
Thus, [tex] m =\frac{t}{s + v} [/tex]
