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

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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

Mathematics
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\(\Large y^2 + 7y + 12\) factors to what?
(Y+3)(Y+4)?
correct

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\(\Large y^2 - 3y - 18\) factors to what?
(y-6)(y+3) not sure about that one
it's correct
ok, so what do i do next? cancel out (y+3)?
Why did we do all that? We factor everything, then we cancel the common (y+3) terms \[\Large \frac{y^2+7y+12}{y^2-3y-18}\] \[\Large \frac{(y+3)(y+4)}{y^2-3y-18}\] \[\Large \frac{(y+3)(y+4)}{(y-6)(y+3)}\] \[\Large \frac{\color{red}{(y+3)}(y+4)}{(y-6)\color{red}{(y+3)}}\] \[\Large \frac{\color{red}{\cancel{(y+3)}}(y+4)}{(y-6)\color{red}{\cancel{(y+3)}}}\] \[\Large \frac{y+4}{y-6}\] ------------------------------------------------------- So \(\Large \frac{y^2+7y+12}{y^2-3y-18}\) simplifies to \(\Large \frac{y+4}{y-6}\)
yes that's correct
thank you so much!!!!
you're welcome

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