Question

PLEASE HELP ME UNDERSTAND THIS !

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

Answer 1

(y^2-y-12)/(y^2 +8y + 15) is this how the problem looks?

Answer 2

Yes

Answer 3

What do you get when you factor y^2-y-12

Answer 4

factor them both. Hint: they share a common factor of (y+3)

Answer 5

(y+3) + (y-4) ?

Answer 6

it should be (y+3)(y-4)

you can check by multiplying them out again

(y+3)(y-4) = y(y-4) + 3(y-4)

(y+3)(y-4) = y^2 - 4y + 3y - 12

(y+3)(y-4) = y^2 - y - 12

Answer 7

what does y^2 +8y + 15 factor to?

Answer 8

(y+5)(y+3) ?

Answer 9

good

Answer 10

\[\Large \frac{y^2-y-12}{y^2 +8y + 15}\]
\[\Large \frac{(y+3)(y-4)}{y^2 +8y + 15}\]
\[\Large \frac{(y+3)(y-4)}{(y+3)(y+5)}\]
\[\Large \frac{\cancel{(y+3)}(y-4)}{\cancel{(y+3)}(y+5)}\]
\[\Large \frac{y-4}{y+5}\]

Answer 11

oh okay, thank you so much. I really appreciate the help. c;

Answer 12

yw