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anonymous

  • one year ago

need help simplifying complex fractions.... :( please help... i made an attempt.. dont just post the answer please teach me how to....

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    it's all about making the the bottom fraction 1... just a sec

  3. anonymous
    • one year ago
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    ya i get that but i confuse myself... i know you need a common demnominator..

  4. anonymous
    • one year ago
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    ugh i keep messing uppppp

  5. anonymous
    • one year ago
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    for yours, you have to get simple fraction over simple fraction first...

  6. anonymous
    • one year ago
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    \[\frac{ 2-\frac{ 4 }{ x+2 } }{5+\frac{ 10 }{ x+2 } }\] is what you have but you need a simple fraction over a simple fraction. to get this, we start with a common denominator for the top expression... \[2-\frac{ 4 }{ x+2 }=2\left( \frac{ x+2 }{ x+2 } \right)-\frac{ 4 }{ x+2 }=\frac{ 2x+4 }{ x+2 }-\frac{ 4 }{ x+2 }=\frac{ 2x }{ x+2 }\] does this make sense?

  7. anonymous
    • one year ago
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    yes that makes sense

  8. anonymous
    • one year ago
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    so you do the same to the bottom fraction?

  9. anonymous
    • one year ago
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    so now we do the same with the bottom expression. Would you like to try?

  10. anonymous
    • one year ago
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    yes give me a min to do it

  11. anonymous
    • one year ago
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    okay

  12. anonymous
    • one year ago
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    |dw:1440524508903:dw|

  13. anonymous
    • one year ago
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    excuse the terrible penmanship lol

  14. anonymous
    • one year ago
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    very good!!!

  15. anonymous
    • one year ago
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    so now we have \[\Large{\frac{ \frac{ 2x }{ x+2 } }{ \frac{ 5x+20 }{ x+2 } }}\] right?

  16. anonymous
    • one year ago
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    |dw:1440524931675:dw|

  17. anonymous
    • one year ago
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    and then i do this?

  18. anonymous
    • one year ago
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    yes, do you know why?

  19. anonymous
    • one year ago
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    because its like dividing regular fractions... you flip and multiply... sooo the (x+2) crosses out right?

  20. anonymous
    • one year ago
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    well, the idea is to make an equivalent expression that is a simple fraction rather than a complex fraction. This is because we humans have a much easier time understanding what a simple fraction represents compared to a complex fraction. to make a simple fraction from a complex fraction, we simply manipulate the bottom fraction so that it is 1. we do this by multplying by the reciprocal of the bottom fraction, like this... \[\Large{\frac{ \frac{ 2x }{ x+2 } }{ \frac{ 5x+20 }{x+2 } }=\frac{ \frac{ 2x }{ x+2 }\cdot \left( \frac{ x+2 }{ 5x+20 } \right) }{ \frac{ 5x+20 }{x+2 }\cdot \left( \frac{ x+2 }{ 5x+20 } \right)}=\frac{ \frac{ 2x }{ x+2 }\cdot \left( \frac{ x+2 }{ 5x+20 } \right) }{ \normalsize{1}}}\]

  21. anonymous
    • one year ago
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    anything over 1 is just itself so that's why we end up with \[\frac{ 2x }{ x+2 }\cdot \frac{ x+2 }{ 5x+20 }\] and we simplify from there

  22. anonymous
    • one year ago
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    does that make sense?

  23. anonymous
    • one year ago
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    yes so you factor 5x+20... to get 5(x+4)

  24. anonymous
    • one year ago
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    \[\frac{ 2x }{ 5(x+4)}\] is the answer

  25. anonymous
    • one year ago
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    or should i not factor it?

  26. anonymous
    • one year ago
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    oh waiiittt hold on

  27. anonymous
    • one year ago
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    wait nvm thats my final answer lol

  28. anonymous
    • one year ago
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    to factor or not to factor is a matter of preference... you still have reduced to lowest terms.

  29. anonymous
    • one year ago
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    but does the process make sense to you?

  30. anonymous
    • one year ago
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    yeah it makes sense to focus on the numerator and denominator separately before you put it all together.. i was trying to do it all in one stepp. so thats my final correct answer?

  31. anonymous
    • one year ago
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    yep

  32. anonymous
    • one year ago
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    good job!

  33. anonymous
    • one year ago
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    thank you for actually teaching me.. no one else takes the time to do that i have 5 more to do lol. but would you be willing to check one of them for me after i do it.

  34. anonymous
    • one year ago
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    sure

  35. anonymous
    • one year ago
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  36. anonymous
    • one year ago
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    and i think that can be reduced?

  37. anonymous
    • one year ago
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    correct, it can be reduced

  38. anonymous
    • one year ago
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    well this is a silly brain fart but i would reduce all the terms by 2?

  39. anonymous
    • one year ago
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    \[\frac{ 4x-12 }{ 5x}\]

  40. anonymous
    • one year ago
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    yep, that's the extent of it

  41. anonymous
    • one year ago
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    one more question lol

  42. anonymous
    • one year ago
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  43. anonymous
    • one year ago
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    for the first question the denominator isnt a fraction...

  44. anonymous
    • one year ago
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    you can make it one... \[5+a=\frac{ 5+a }{ 1 }\]

  45. anonymous
    • one year ago
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    ohhhh wait i got thiis

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  46. anonymous
    • one year ago
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    yes except it is \(25-a^2 \text{ not } a^2 - 25\)

  47. anonymous
    • one year ago
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    gotchaaa.. but does the order i write it affect it? i thought it was a difference of squares either way

  48. anonymous
    • one year ago
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    true, but \(25-a^2 \ne a^2-25\) unless \(a=\pm 5\)

  49. anonymous
    • one year ago
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    ahh i gotchaa. seriously thank you so much! youre amazingg! i might message you when im in need of a lesson lol

  50. anonymous
    • one year ago
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    right on! good luck, have a great day and keep on learning!

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