Question

Solve 1/F=1/m+1/p for m

Answer 1

multiply everything out by m:
m/F = 1 + m/p

Answer 2

Move all the terms with m to one side:
m/F - m/p = 1

Answer 3

pull out an m:
m(1/F - 1/p) = 1

Answer 4

Divide both sides by 1/F-1/p:
m = 1/(1/F-1/p). Now just do some simplification to get your answer.