What is this answer ? please show steps.

Question

find (g(x+h)-g(x))/h of g(x)=((-2)/(x-3))

Answer 1

g(x+h) = -2/(x+h-3)

[g(x+h) - g(x)] / h = [-2/(x+h-3) + 2/(x-3)] / h

= [-2x + 6 + 2x + 2h - 6] / [h(x+h-3)(x-3)] (putting two numerator fractions over a common denominator)

= 2h / [h(x+h-3)(x-3)]

= 2 / [(x+h-3)(x-3)] , for h ≠ 0