Question 1065973: Please can you rearrange the following to make u the subject of the formula
1/u + 1/v = 1/f
Many thanks.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1/u + 1/v = 1/f
multiply both sides of the equation by uvf.
you will get uvf/u + uvf/v = uvf/f
simplify to get vf + uf = uv
subtact uf from both sides of the equation to get vf + uf - uf = uv - uf
simplify to get vf = uv - uf
factor out the u on the right hand side of the equation to get vf = u * (v - f)
divide both sides of the equation by (v - f) to get vf / (v - f) = u * (v - f) / (v - f)
simplify to get vf / (v - f) = u
solve for u to get u = vf / (v - f)
i believe that's as simple as it can get.
you can confirm by replacing u with vf / (v - f) in the original equation and evaluating it.
you will get v/vf = v/vf.
since this is true, the solution looks good.
alternatively, you can give u, v, and f arbitrary values and evaluate both the original equation and the final equation to see if the answers agree.
for example:
u = 2
v = 3
solve this equation and you get f = 6/5.
you get 1/2 + 1/3 = 1/(6/5)
combine like terms on the left and you get 5/6 = 1/(6/5)
multiply both sides of the equation by 6/5 and you get 5/6 * 6/5 = 1/(6/5) * (6/5) which becomes 30/30 = 1 which is true.
now do the same with the final equation, by making u = 2, v = 3, and f = 6/5.
start with u = vf / (v - f)
u = 2
v = 3
f = 6/5
your equation becomes 2 = (3 * 6/5) / (3 - 6/5).
simplify to get 2 = (18/5) / (15/5 - 6/5) which becomes:
2 = (18/5) / (9/5).
this is equivalent to 2 = 18/5 * 5/9.
this can be simplified to 2 = 18/9 which is equal to 2.
since 2 = 2, the equation is true, and the solution is confirmed to be good.
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