Adding fractions...?

Question

3x/(x^2-x-6) + (x+2) / (x^2-6x+9)

so this is a fraction added to another fraction.

thanks in advance
this is really confusing

Answer 1

x ² - x - 6 = ( x - 3 ) ( x + 2 )
x ² - 6 x + 9 = ( x - 3 ) ²

3x / ( x - 3 ) ( x + 2 ) + ( x + 2 ) / ( x - 3 ) ²
3x (x - 3) + (x + 2) (x + 2) / [ (x - 3) ² (x + 2) ]
( 3 x ² - 9 x + x ² + 4 x + 4 ) / [ (x - 3) ² (x + 2) ]
(4 x ² - 5 x + 4) / [ (x - 3) ² (x + 2) ]

Answer 2

(x^2-x-6) can be simplified as
(x-3)(x+2)

(x^2-6x+9) can be simplified as
(x-3)(x-3)

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

take x-3 common
(3x/(x+2)+(x+2)/(x-3))/(x-3)
take LCM
3x(x-3)+(x+2)^2/(x-3)(x-3)(x+2)

4x^2-5x+4/(x-3)(x-3)(x+2)