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Bananas1234

  • one year ago

Simplify. u^2-4/u^2 - 2u

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  1. nikato
    • one year ago
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    |dw:1433048410396:dw| is this your question?

  2. anonymous
    • one year ago
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    you can factorize u^2-4 to (u-2)(u+2) and next exp as u(u-2) cancel out (u-2) from denom and num

  3. Bananas1234
    • one year ago
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    u + 2, u is not 2?

  4. UsukiDoll
    • one year ago
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    we have a perfect square on the numerator... can we split that up in the form of (a+b)(a-b) where a = x and b =2?!

  5. Bananas1234
    • one year ago
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    i dont think so, can we?

  6. UsukiDoll
    • one year ago
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    whatttttttttttttttttttt! pop quiz what the square root of 4

  7. Bananas1234
    • one year ago
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    2

  8. UsukiDoll
    • one year ago
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    yes... whenever we have a perfect square we can split (a^2-b^2) in the form of (a+b)(a-b)

  9. UsukiDoll
    • one year ago
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    so since a = x and b = 2 what is the numerator... we can split it up in the form of (a+b)(a-b)

  10. UsukiDoll
    • one year ago
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    a = x =u b = 2

  11. Bananas1234
    • one year ago
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    i see

  12. Bananas1234
    • one year ago
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    so what do i do next

  13. UsukiDoll
    • one year ago
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    what do you have for the numerator first?

  14. Bananas1234
    • one year ago
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    u + 2?

  15. UsukiDoll
    • one year ago
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    no you're missing something I'll give an example (x^2-9) =(x+3)(x-3) now follow that pattern with u^2-4

  16. UsukiDoll
    • one year ago
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    it's 3 on the example because the square root of 9 is 3

  17. Bananas1234
    • one year ago
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    i am not sure i am following you

  18. UsukiDoll
    • one year ago
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    (u^2-4) the term u^2 is a perfect square and the same goes for 4 so the square root of u^2 is u and the square root of 4 is 2 whenever we have something like u^2 - 4 , it is a perfect square polynomial in the form of (u^2-4) = (u+2)(u-2)

  19. Bananas1234
    • one year ago
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    ok

  20. UsukiDoll
    • one year ago
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    now for the denominator u^2 can also be written as uu... eventually you may be required to be swift in factoring and taking out like terms u^2-2u I can take a u out and it becomes u(u-2) to see it easier uu-2u and since we have a u on the left and u on the right we can take that out

  21. Bananas1234
    • one year ago
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    ok

  22. UsukiDoll
    • one year ago
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    so now we have (u+2)(u-2) / u(u-2) so what does the numerator and denoiminator have in common that we can remove.

  23. Bananas1234
    • one year ago
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    u-2

  24. UsukiDoll
    • one year ago
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    yes! so we have (u+2)/(u)

  25. Bananas1234
    • one year ago
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    i think i understand better now

  26. UsukiDoll
    • one year ago
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    hmm if we have to simplify further we can split (u+2)/(u) into 2 fractions because they have the same denominator u/u +2/u 1+ 2/u or we can leave the answer like that

  27. Bananas1234
    • one year ago
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    based on my options i think its ok to leave it

  28. UsukiDoll
    • one year ago
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    yeah that's fine ^^

  29. Bananas1234
    • one year ago
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    so is it u +2/u, u is not 0 or u +2/u, u is not 2, u is not 0 ? and how do i find out?

  30. Bananas1234
    • one year ago
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    @UsukiDoll

  31. UsukiDoll
    • one year ago
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    the denominator of u is the whole entire thing \[\frac{u+2}{u}\]

  32. UsukiDoll
    • one year ago
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    since they share a single denominator we can split it up into 2 different fractions or leave it as is.

  33. UsukiDoll
    • one year ago
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    \[\frac{u}{u} +\frac{2}{u} \rightarrow 1 + \frac{2}{u}\]

  34. UsukiDoll
    • one year ago
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    we can't have u = 0 .. because anything divided by 0 is undefined.

  35. Bananas1234
    • one year ago
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    i see

  36. Bananas1234
    • one year ago
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    Thanks

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