Simplify into one fraction 3x 2 5x 3 8x 19x 2x 3 8x 2

Simplify into one fraction. -3/x + 2 - -5/x + 3 -8x - 19/(x + 2)(x + 3) -8/(x + 2)(x + 3) 2/(x + 2)(x + 3) 2x + 1/(x + 2)(x + 3)

Solution

(-3/(x + 2)) - (-5/(x + 3))

= (5/(x + 3)) - (3/(x + 2))

= [5*(x + 2) - 3*(x + 3)]/((x + 3)*(x + 2))

= (5x + 10 - 3x - 9)/((x + 3)*(x + 2))

= (2x + 1)/((x + 3)*(x + 2))

Correct option is D.