h/5=(h-3)/(h+1)+12/(5h+5).
The LCD is 5h+5 so multiply through by it:
h(h+1)=5(h-3)+12,
h2+h=5h-15+12,
h2-4h+3=0=(h-3)(h-1) so h=3 or 1. If we reject h=3 (as advised) we are left with h=1 as the solution.
Let's check it:
1/5=-2/2+12/10,
1/5=-1+6/5 which is true. So h=1 is a solution.
h=3 could have been a solution:
3/5=0+12/20 which is true.