Explanation:
first I would suggest finding a common denominator for both fractions and then extract it as a common factor :
(x-2)(x+6) could be the common denominator and we get
(2x+3)/((x-2)(x+6)) + 2(2x-1)(x+6)/((x-2)(x+6))
extracting the denominator :
(1/((x-2)(x+6))) × ((2x+3) + 2(2x-1)(x+6))
and now doing all the calculations :
(1/((x-2)(x+6))) × (2x+3 + (4x-2)(x+6))
(1/((x-2)(x+6))) × (2x+3 + 4x² + 24x - 2x - 12)
(1/((x-2)(x+6))) × (4x² + 24x - 9)
(1/(x² + 6x - 2x - 12)) × (4x² + 24x - 9)
(4x² + 24x - 9) / (x² + 4x - 12)