Iwill give ! what is the simplified form of the quantity y−squared minus y minus 12 over the quantity y−squared plus 8y plus 15?

Usually you want to factor the numerator and denominator expressions to simplify your rational expression.
  (y² -y -12)/(y² +8y +15)
  = (y-4)(y+3)/((y+5)(y+3))

A common factor of y+3 can be removed from numerator and denominator.
  = (y-4)/(y+5) . . . . . . with the restriction y≠-3


To factor these, you are looking for factors of -12 that add to -1:
  -12 = -1*12 = -2*6 = -3*4 = -4*3 = -6*2 = -12*1
The pair that adds to -1 is {-4, 3}.

And you are looking for factors of 15 that add to 8:
  15 = 1*15 = 3*5
The pair that adds to 8 is {3, 5}.