(x+2/x+3)/(x^2+x-12/x^2-9) simplify?

(x + 2/ x + 3)/(x^2 + x - 12 / x^2 - 9)

= (x + 2) (x^2 - 9) / (x + 3) (x^2+x-12)

= (x + 2) (x + 3) ( x - 3) / (x + 3) (x - 3) (x + 4)

= (x + 2) / (x + 4)

(x + 2) / (x + 4)

x^2 + x - 12 = (x+4)(x-3)
x^2 - 9 = (x + 3)(x - 3)

When dividing fraction, you invert the denominator and change to multiplication, so the expression is

[(x+2)/(x+3)] * [(x +3)(x-3)/(x+4)(x-3)]

Cancelling the (x + 3) and the (x - 3), we have

(x+2)/ (x + 4)

(x + 2)(x² - 9)
---------------------------
(x + 3)(x² + x - 12)

(x + 2)(x - 3)(x + 3)
------------------------------
(x + 3) (x + 4)(x - 3)

x + 2
---------
x + 4

(x+2/x+3)
-------------------
(x^2+x-12/x^2-9)

= Use crossing times

= (x+2)/(x+3) times (x^2-9)/(x^2+x-12)

= (x+2) . (x-3)(x+3)
--------------------------
(x+3) (x-3) (x+4)

= eliminate (x+3)(x-3)

= (x+2) / (x+4)

(x + 2/x + 3)/(x^2 + x - 12/x^2 - 9)
= [(x + 2)/(x + 3)][1/(x + 4)(x - 3)/(x + 3)(x - 3)]
= [(x + 2)/(x + 3)][(x + 3)(x - 3)/(x + 4)(x - 3)] (cancel out x - 3)
= [(x + 2)/(x + 3)][(x + 3)/(x + 4)]
= (x + 2)(x + 3)/(x + 3)(x + 4) (cancel out x + 3)
= (x + 2)/(x + 4)