Question

Solve 1/f=1/a+1/b for f? Please help i just don't understand how to do this.

Answer 1

`f = (ab)/(a+b)`

Explanation:

When we say "solve for `f`", we mean you should isolate `f` on one side of the equation, so you have something of the form `f = ...`.

We wish to solve `1/f = 1/a + 1/b` for `f`. For reasons that will become clear, we need to make the right-hand side (RHS) of the equation a single fraction. We do this by finding a common denominator.

`1/a + 1/b`
`= b/(ab) + a/(ab)`
`= (a+b)/(ab)`

So we have `1/f = (a+b)/(ab)`. Multiply both sides by `f` to give `1 = f ((a+b)/(ab))`. Now multiply both sides by `ab` to give `ab = f(a+b)`. Finally, divide both sides by `a+b` to give `(ab)/(a+b) = f`.

Thus, our final answer is `f = (ab)/(a+b)`.