Greetings!
"Solve for f: [tex]1/f=1/x+1/y[/tex]".
Multiply both sides by f.
[tex](1/f)*f=(1/x+1/y)*f[/tex]
Simplify.
[tex]1=(fx+fy)/xy[/tex]
Multiply both sides by xy.
[tex](1)*xy=((xf+yf)/xy)*xy[/tex]
Simplify.
[tex]xy=xf+yf[/tex]
Factor out f.
[tex]xy=f(x+y)[/tex]
Divide both sides by x+y.
[tex](xy)/x+y=(f(x+y))/x+y[/tex]
Simplify.
[tex](xy)/(x+y)=f[/tex]
[tex]f=(xy)/(x+y)[/tex]
Had to change the variable as Brainly thought it was a swearword. Sorry.
Hope this helps.
-Benjamin
