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anonymous

  • one year ago

Find the sum and simplify and show all work and steps please..will give medals!! 2x/( x^2-x-12) + 3/ (x^2+4x+3)

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  1. Mertsj
    • one year ago
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    Factor both denominators for the first step

  2. Mertsj
    • one year ago
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    What are the factors of x^2-x-12 ?

  3. anonymous
    • one year ago
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    I have no idea. Im very confused with this question

  4. Mertsj
    • one year ago
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    |dw:1442887631832:dw|

  5. Mertsj
    • one year ago
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    Think of two numbers whose product is -12

  6. anonymous
    • one year ago
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    6 & -2?? 12 & -1 ??

  7. Mertsj
    • one year ago
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    When you add the two numbers, you have to get -1 so think of some more possibilities.

  8. anonymous
    • one year ago
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    4 & -3

  9. Mertsj
    • one year ago
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    4+(-3)=1 The sum must be -1

  10. anonymous
    • one year ago
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    -4 & 3

  11. Mertsj
    • one year ago
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    Good.

  12. Mertsj
    • one year ago
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    |dw:1442887952257:dw|

  13. Mertsj
    • one year ago
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    So now you have factored the first denominator. Try the second one.

  14. anonymous
    • one year ago
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    X^2+4x+3 = (x+3)(x+1)

  15. Mertsj
    • one year ago
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    So now we have this problem: \[\frac{2x}{(x-4)(x+3)}+\frac{3}{(x+1)(x+3)}\]

  16. Mertsj
    • one year ago
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    Now we have to get the common denominator so we can add the two fractions.

  17. Mertsj
    • one year ago
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    For the first denominator we need the factors (x-4)(x+3) For the second denominator we need the factors (x+1)(x+3)

  18. Mertsj
    • one year ago
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    So the factors we need are (x-4) and (x+3) and (x+1) and that is the common denominator. Are you with me so far?

  19. anonymous
    • one year ago
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    Yes

  20. Mertsj
    • one year ago
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    So the first fraction will have to be multiplied by (x+1)/(x+1) to get the denominator right.

  21. Mertsj
    • one year ago
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    The second fraction will have to be multiplied by (x-4)(x-4) to get the denominator right. Do you agree?

  22. anonymous
    • one year ago
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    Yes

  23. Mertsj
    • one year ago
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    \[\frac{2x}{(x-4)(x+3)}\times \frac{(x+1)}{(x+1)} + \frac{3}{(x+1)(x+3)}\times \frac{(x-4)}{(x-4)}\]

  24. Mertsj
    • one year ago
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    So now if we do the multiplication we have:

  25. Mertsj
    • one year ago
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    \[\frac{2x^2+2x+3x-12}{(x+1)(x+3)(x-4)}\]

  26. Mertsj
    • one year ago
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    Still ok with this?

  27. anonymous
    • one year ago
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    Yes

  28. Mertsj
    • one year ago
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    So let's add the like terms and finish up.

  29. Mertsj
    • one year ago
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    \[\frac{2x^2+5x-12}{(x+1)(x+3)(x-4)}\]

  30. anonymous
    • one year ago
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    Is that the final answer?? It doesnt simplify down anymore??

  31. Mertsj
    • one year ago
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    You could try to factor the numerator but I don't think it will factor. Are there factors of -24 whose sum is 5?

  32. anonymous
    • one year ago
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    I dont think so. The correct answer would be 2x^2+5x-12 / (x+1)(x+3)(x-4) ?

  33. Mertsj
    • one year ago
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    Oh it will factor. The factors are (2x-3)(x+4)

  34. Mertsj
    • one year ago
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    So now we have: \[\frac{(2x-3)(x+4)}{(x+1)(x+3)(x-4)}\]

  35. Mertsj
    • one year ago
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    But there are no common factors to cancel so our answer is correct.

  36. anonymous
    • one year ago
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    So the (2x-3)(x+4) and so on the correct answerr??

  37. Mertsj
    • one year ago
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    The answer is: \[\frac{2x^2+5x-12}{(x+1)(x+3)(x-4)} or \frac{(2x-3)(x+4)}{(x+1)(x+3)(x-4)}\]

  38. Mertsj
    • one year ago
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    because they are two forms of the same answer

  39. Mertsj
    • one year ago
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    So you can take your pick.

  40. anonymous
    • one year ago
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    Oh okay i understand (: thank you so much!

  41. Mertsj
    • one year ago
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    yw

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