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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?

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  1. anonymous
    • one year ago
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    |dw:1438784510372:dw|

  2. DanJS
    • one year ago
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    to combine those, multiply both of them by a ratio of the common denominator, (2x + 3)(x+2)

  3. anonymous
    • one year ago
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    ... im confused

  4. DanJS
    • one year ago
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    |dw:1438785227000:dw|

  5. DanJS
    • one year ago
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    THe common denominator is (2x+3)(x+3), Just multiplied the original expression by 1, the common denominator over itself

  6. anonymous
    • one year ago
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    What does that do to add them together?

  7. DanJS
    • one year ago
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    When you multiply that out, both will be over the same denominator, so you can add them together

  8. DanJS
    • one year ago
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    \[\frac{ (x+9)(x+2) }{ (2x+3)(x+2) }+\frac{ (x+4)(2x+3) }{ (2x+3)(x+2) }\]

  9. anonymous
    • one year ago
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    okay, so when you have the same denominator you just add the numerators together,correct?

  10. DanJS
    • one year ago
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    right, you need the same denominators

  11. anonymous
    • one year ago
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    will the denominator for this one be 2x^2+7x+6?

  12. DanJS
    • one year ago
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    yes, but i would leave that as it is before

  13. DanJS
    • one year ago
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    \[\frac{ (x+9)(x+2)+(x+4)(2x+3) }{ (2x+3)(x+2) }\]

  14. anonymous
    • one year ago
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    the answer choice has it out how i wrote it

  15. DanJS
    • one year ago
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    oh k, yeah you can try expanding everything out and combining like terms in the numerator too.

  16. anonymous
    • one year ago
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    would the numerator be 2x+13?

  17. DanJS
    • one year ago
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    Reason i said leave the denominator, sometimes the numerator will give a factor that will cancel

  18. DanJS
    • one year ago
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    the numerator goes to \[x^2+11x+18+2x^2+3x+8x+12\] then just combine

  19. DanJS
    • one year ago
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    \[\frac{ 3x^2+22x+30 }{ (2x+3)(x+2) }\]

  20. anonymous
    • one year ago
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    thank you!

  21. DanJS
    • one year ago
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    you get how to do those probs now?

  22. DanJS
    • one year ago
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    welcome

  23. anonymous
    • one year ago
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    yes, one question though.. If this were subtraction how would it change what you did?

  24. DanJS
    • one year ago
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    \[\frac{ (x+9)(x+2)-(x+4)(2x+3) }{ (2x+3)(x+2) }\] it would change the sign on all the terms that are expanded (-1)(x+4)(2x+3)

  25. DanJS
    • one year ago
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    - (2x^2 +11x + 12) -2x^2 - 11x - 12

  26. anonymous
    • one year ago
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    it wouldn't change what you did to the denominator?

  27. DanJS
    • one year ago
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    nope, same thing

  28. anonymous
    • one year ago
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    okay, thank you !

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