Rearranging formulae

Rearrange 1/u + 1/v = 1/f

to make u the subject of the formula. Give your answer in its simplest form.

There are a number of ways to approach this problem.

By subtracting 1/v on both sides we get 1/u as the subject of the equation:

1/u = 1/f - 1/v

The inverse of the equation can be found to make the subject u:

u = 1/(1/f - 1/v)

This can be simplified by multiplying by fv/fv:

u(fv/fv) = fv/(fv/f - fv/v)

As fv/fv is equal to one, this can be simplified further to give the final answer:

u = fv/(v-f)