anonymous one year ago What is the simplified form of the quantity of x plus 9, all over the quantity of 2x plus 3 + the quantity of x plus 4, all over the quantity of x plus 2?

1. anonymous

|dw:1438784510372:dw|

2. DanJS

to combine those, multiply both of them by a ratio of the common denominator, (2x + 3)(x+2)

3. anonymous

... im confused

4. DanJS

|dw:1438785227000:dw|

5. DanJS

THe common denominator is (2x+3)(x+3), Just multiplied the original expression by 1, the common denominator over itself

6. anonymous

What does that do to add them together?

7. DanJS

When you multiply that out, both will be over the same denominator, so you can add them together

8. DanJS

$\frac{ (x+9)(x+2) }{ (2x+3)(x+2) }+\frac{ (x+4)(2x+3) }{ (2x+3)(x+2) }$

9. anonymous

okay, so when you have the same denominator you just add the numerators together,correct?

10. DanJS

right, you need the same denominators

11. anonymous

will the denominator for this one be 2x^2+7x+6?

12. DanJS

yes, but i would leave that as it is before

13. DanJS

$\frac{ (x+9)(x+2)+(x+4)(2x+3) }{ (2x+3)(x+2) }$

14. anonymous

the answer choice has it out how i wrote it

15. DanJS

oh k, yeah you can try expanding everything out and combining like terms in the numerator too.

16. anonymous

would the numerator be 2x+13?

17. DanJS

Reason i said leave the denominator, sometimes the numerator will give a factor that will cancel

18. DanJS

the numerator goes to $x^2+11x+18+2x^2+3x+8x+12$ then just combine

19. DanJS

$\frac{ 3x^2+22x+30 }{ (2x+3)(x+2) }$

20. anonymous

thank you!

21. DanJS

you get how to do those probs now?

22. DanJS

welcome

23. anonymous

yes, one question though.. If this were subtraction how would it change what you did?

24. DanJS

$\frac{ (x+9)(x+2)-(x+4)(2x+3) }{ (2x+3)(x+2) }$ it would change the sign on all the terms that are expanded (-1)(x+4)(2x+3)

25. DanJS

- (2x^2 +11x + 12) -2x^2 - 11x - 12

26. anonymous

it wouldn't change what you did to the denominator?

27. DanJS

nope, same thing

28. anonymous

okay, thank you !

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