How is 1/(x-2) = (2x - 6)/(x + 6) + 1 rewritten as 1/(x - 2) = 3x/(x + 6)? I don't understand.

Answer 1

right side
= (2x-6)/(x+6) + 1
= (2x-6)/(x+6) + (x+6)/(x+6)
now we have a common denominator
= (2x-6 + x+6)/(x-6
= 3x/(x+6)
as you required.