To simplify the expression (P^2 - g^2) / (3p + 3g), we first factor the numerator:

P^2 - g^2 = (P+g)(P-g)

Now the expression becomes:

((P+g)(P-g)) / (3p + 3g)

Factoring out a 3 from the denominator:

((P+g)(P-g)) / 3(P + g)

Now we can cancel out the common factor (P+g) from the numerator and denominator to get the simplified expression:

(P-g) / 3