Could you please explain how to come to the answer.

Question

Determine the number of solutions (P,Q) for the equation (P/Q) - (Q/P) = ((P+Q) / (PQ)) where P and Q are integers, from -8, to +8 inclusive.

Answer 1

By making the left side have common denominator PQ, you will get P² - Q² as the numerator on the left side.

Then equating numerators, you see that (P-Q)(P+Q) = P+Q so that P-Q must equal 1 subject to the condition that PQ ≠0.

 

This forms the basis of your further evaluation (study); you can take it from here. I suggest a tabular approach.