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)#.