A binary operation * is defined by a*b = ab+a+b for any real number a and b. if the identity element is zero, find the inverse of 2 under this operation.

Factorize completely \(x^{2} + 2xy + y^{2} + 3x + 3y - 18\).

Three consecutive positive integers k, l and m are such that l\(^2\) = 3(k+m). Find the value of m.

Express \(\frac{1}{x^{3}-1}\) in partial fractions