Shunyam Samyasamuccaye
When the sum is the same, that sum is zero (shun · yam sam · ya · sa · muc · ca · ye)
What it means
Spot equations that look hard but secretly contain a repeated piece on both sides. Once you spot it, the equation collapses to something you can solve in your head.
Worked example
Solve 1/(x+3) + 1/(x+5) = 1/(x+1) + 1/(x+7). Add the bottoms on the left: (x+3) + (x+5) = 2x + 8. Add the bottoms on the right: (x+1) + (x+7) = 2x + 8. They're equal — so the rule says 2x + 8 = 0, giving x = −4.