What is the simplified form of the quantity y-squared plus 7y plus 12 over the quantity y-squared plus 8y plus 15

Firstly, let's factorise each equation individually - to do this, find 2 numbers that when summed add to the value of the second term, and when multiplied give the value of the third term.

7 and 12 give us 4 and 3 (4+3=7, 4*3=12) - - 8 and 15 give us 5 and 3 (5+3=8, 5*3=15)

Now we can rewrite these equations as (y+4) (y+3) and (y+5) (y+3) respectively.

Putting this in a fraction: (y+4) (y+3) / (y+5) (y+3) - - We can clearly see that there is a y+3 on both sides of the fraction, and given there are no terms outside of the brackets being multiplied, we can directly cancel.

This gives us our final answer:

(y+4) / (y+5)