## anonymous one year ago 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

1. jim_thompson5910

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

2. anonymous

(Y+3)(Y+4)?

3. jim_thompson5910

correct

4. jim_thompson5910

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

5. anonymous

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

6. jim_thompson5910

it's correct

7. anonymous

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

8. jim_thompson5910

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 $$\Large \frac{y+4}{y-6}$$

9. jim_thompson5910

yes that's correct

10. anonymous

thank you so much!!!!

11. jim_thompson5910

you're welcome