Question

What is the simplified form of the quantity y-squared plus 7y plus 12 over the quantity y-squared minus 3y minus 18 ?

Answers:
y minus 4 over y minus 6
y minus 4 over y plus 6
y plus 4 over y minus 6
y plus 4 over y plus 6

Answer 1

\(\Large y^2 + 7y + 12\) factors to what?

Answer 2

(Y+3)(Y+4)?

Answer 3

correct

Answer 4

\(\Large y^2 - 3y - 18\) factors to what?

Answer 5

(y-6)(y+3) not sure about that one

Answer 6

it's correct

Answer 7

ok, so what do i do next? cancel out (y+3)?

Answer 8

Why did we do all that? We factor everything, then we cancel the common (y+3) terms
\[\Large \frac{y^2+7y+12}{y^2-3y-18}\]
\[\Large \frac{(y+3)(y+4)}{y^2-3y-18}\]
\[\Large \frac{(y+3)(y+4)}{(y-6)(y+3)}\]
\[\Large \frac{\color{red}{(y+3)}(y+4)}{(y-6)\color{red}{(y+3)}}\]
\[\Large \frac{\color{red}{\cancel{(y+3)}}(y+4)}{(y-6)\color{red}{\cancel{(y+3)}}}\]
\[\Large \frac{y+4}{y-6}\]
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So \(\Large \frac{y^2+7y+12}{y^2-3y-18}\) simplifies to \(\Large \frac{y+4}{y-6}\)

Answer 9

yes that's correct

Answer 10

thank you so much!!!!

Answer 11

you're welcome