Re-arranging formulae?

1/f = 1/u + 1/v
1/f = v/uv + u/uv
1/f = (v+u)/uv
f = uv / (v+u)

1/f = (v+u)/uv
First multiply both sides by uv.
uv/f = v+u
Then multiply both sides by f.
uv = f(v+u)
uv = fv + fu
uv-fv = fu
and now the most important step - factorising
(u-f)v = fu
v = fu / (u-f)

N.B. these formulas are used for working out focal lengths of lenses.

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

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

therefore
1/f = (u+v)/uv
and so f = ((u+v)/uv)^-1
f = vu/(v+u)
and to make c the subject,
1/v = 1/f - 1/u
1/v = (u-f)/uf
v = ((u-f)/uf)^-1
v = uf/(u-f)

1/f = (u + v)/uv, so f = uv/(u + v)
v works similarly, with a minus sign thrown in.

1/f = 1/u + 1/v
1/u = 1/f - 1/v
multiply both sides by fv, you get:
fv/u = v - f
u = fv/(v - f)

Hint: add fractions normally.

You can't make two things the subject of the formula. The formula has one subject.

1 = f/u + f/v

uv = fv/uv + fu/uv

uv = (fv + fu)/uv

(uv)^2 = fv + fu

(uv)^2 = f(v + u)

f = (uv)^2/(v + u)

You can keep shoving terms around to get v as the subject.