1/f=1/d-1/h to solve for h.
Multiply both sides by fdh:
dh=fh-fd, fd=fh-dh.
Take out the common factor h (that is, factorise the RHS):
fd=h(f-d), fd/(f-d)=h or h=fd/(f-d).
Another way:
1/f=1/d-1/h=(h-d)/dh.
Turn both sides upside down:
f=dh/(h-d), f(h-d)=dh, fh-fd=dh, fh-dh=fd.
Take out the common factor h:
h(f-d)=fd, h=fd/(f-d).