Sopantyadvayamantyam

This Sutra is used to find solution of equations in the following form:
1/ ab + 1/ac = 1/ad + 1/bc
where a, b, c and d are in arithmetic progression,
b= a + z
c = a + 2z
d = a + 3z
The solution for such equations is 2c + d = 0.
For example:
1/ (x+1)(x+2) + 1/ (x +1)(x+3) = 1/ (x+1)(x + 4) + 1/ (x+2)(x +3)
Now according to the above Sutra the solution would be:
2(x +3) + (x+4) = 0
2x +6+x+4 =0
3x + 10 =0
x= -10/3