SOLUTION: Make u as the subject in 1/u+ 1/v = 1/f

Question 114486: Make u as the subject in 1/u+ 1/v = 1/f

Found 2 solutions by bucky, MathLover1:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
To solve for u, multiply both sides (all terms) of this equation by the quantity (u*v*f). That
multiplication changes the equation to:
.

.
Next in each of the three terms cancel the denominator with its corresponding factor in
the numerator:
.

.
This reduces the equation to:
.

.
Then collect the terms containing "u" on one side of the equation and get all other terms
on the other side of the equation. You can begin by getting rid of the v*f term on the
left side. Do that by subtracting v*f from both sides to give you:
.

.
Now get rid of the u*v on the right side by subtracting u*v from both sides to give you:
.

.
Just to make things a little "neater" get rid of the negative sign on the right side by
multiplying both sides of the equation (all terms) by -1. This results in:
.

.
Swap the positions of the terms on the left side so the positive term comes first:
.

.
Note that "u" is a common factor of the two terms on the left side. Factor it out and
you have:
.

.
Solve for "u" by dividing both sides of this equation by the quantity (v - f) because that
quantity is the multiplier of "u". This division results in:
.

.
And there's the answer.
.
Hope this helps you to see how to "rearrange" and "modify" the original equation to solve for
u ... and I hope that when you said you wanted "u" to be the subject
that you meant you wanted to find what "u" equaled in the terms of the
other unknowns involved.
.
If I am in error, please post your problem again.
.

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Make as the subject in
.........move to the right

.........multiply both sides by
.........
.........
.........divide both sides by
.........

or

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