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smurfy14

  • 5 years ago

[(1/(x^2)-1/Y^2)]/[(1/x^2+2/xy+1/y^2)] plz help! youd be awsome if ya did! (tell me how you get then answer as well, thanks!)

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  1. anonymous
    • 5 years ago
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    What are your instructions for this problem?

  2. smurfy14
    • 5 years ago
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    "simplify complex functions"

  3. anonymous
    • 5 years ago
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    OK, I started by multiplying the top and bottom of the complex fraction by the LCD, which is x^2y^2 in this case

  4. anonymous
    • 5 years ago
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    \[\frac{\frac{1}{x^2}-\frac{1}{2}}{\frac{1}{x^2}+\frac{2}{xy}+\frac{1}{y^2}}\]

  5. anonymous
    • 5 years ago
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    arya has it, just wanted to type it.

  6. anonymous
    • 5 years ago
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    Which came out to (y^2-x^2)/(y^2+2xy+x^2)

  7. anonymous
    • 5 years ago
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    Sorry, haven't figured out how to type all of the nice equations yet

  8. anonymous
    • 5 years ago
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    there is a gimmick here. the denominator is \[(\frac{1}{x}+\frac{1}{y})^2\]

  9. anonymous
    • 5 years ago
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    and the numerator is \[(\frac{1}{x}+\frac{1}{y})(\frac{1}{x}-\frac{1}{y})\]

  10. anonymous
    • 5 years ago
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    so you can cancel.

  11. smurfy14
    • 5 years ago
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    can you explain how multiplying the LCD with the second fraction on the bottom came out to be 2xy?

  12. smurfy14
    • 5 years ago
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    nevermind i got it

  13. anonymous
    • 5 years ago
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    \[(2/xy)timesx ^{2}y ^{2}=2x ^{2}y ^{2}/xy=2\]

  14. smurfy14
    • 5 years ago
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    idk what to do after (y^2-x^2)/(y^2+2xy+x^2)

  15. anonymous
    • 5 years ago
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    Ignore my response, it didn't come out quite right

  16. anonymous
    • 5 years ago
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    Factor

  17. anonymous
    • 5 years ago
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    \[\frac{a^2-b^2}{a+2ab+b^2}=\frac{(a+b)(a-b)}{(a+b)(a+b)}=\frac{a-b}{a+b}\]

  18. anonymous
    • 5 years ago
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    y^2-x^2=(y-x)(y+x) y^2+2xy+x^2=(y+x)(y+x)

  19. anonymous
    • 5 years ago
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    \[\frac{\frac{1}{x}-\frac{1}{y}}{\frac{1}{x}+\frac{1}{y}}\] multiply top an bottom by \[xy\]

  20. anonymous
    • 5 years ago
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    Then we can cancel one of the (y+x)

  21. smurfy14
    • 5 years ago
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    oh ok thanks so much! think you could help me with [a-b]/[a^-1=b^-1]

  22. anonymous
    • 5 years ago
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    Sure

  23. smurfy14
    • 5 years ago
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    imean [a-b]/[a^-1-b^-1]

  24. anonymous
    • 5 years ago
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    OK, a^-1=1/a and b^-1=1/b

  25. anonymous
    • 5 years ago
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    Does that part make sense?

  26. smurfy14
    • 5 years ago
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    no? so ur saying you just move the -1 to the top and not the a along with it?

  27. anonymous
    • 5 years ago
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    Not quite, lets see if it makes more sense when I type out the whole equation. Hang on

  28. anonymous
    • 5 years ago
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    (a-b)/(a^-1-b^-1) = (a-b)/[(1/a)-(1/b)]

  29. anonymous
    • 5 years ago
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    Does that make any more sense or no?

  30. smurfy14
    • 5 years ago
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    oh ok ya that makes sense, so you dont move the a with the 1 im guessing

  31. anonymous
    • 5 years ago
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    \[\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x^2}+\frac{1}{y^2}+\frac{2}{x y}}=1-\frac{2 x}{x+y} \] Both equation sides evaluated at x=11 and y=17 yield the value 3/14. Note: The first "y" from left to right in the problem expression text string is a cap y, Y, not lower case y. Mathematica views the two as different characters. The cap Y was changed to lower case prior to solving the problem.

  32. anonymous
    • 5 years ago
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    Not quite sure what you mean

  33. smurfy14
    • 5 years ago
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    hah nevermind i got it you can keep going :)

  34. anonymous
    • 5 years ago
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    Cool, so then just like the previous problem the next step is to multiply the to and bottom by the LCD, which in this case is ab

  35. anonymous
    • 5 years ago
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    *top

  36. smurfy14
    • 5 years ago
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    so (ab-ab)/(0)?

  37. smurfy14
    • 5 years ago
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    how do you figure out the denominator?

  38. anonymous
    • 5 years ago
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    I got (a-b)ab for the numerator and b-a for the denominator

  39. anonymous
    • 5 years ago
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    To get the denominator: (1/a-1/b)ab (the LCD)=ab/a-ab/b=b-a

  40. smurfy14
    • 5 years ago
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    ok got it so how did you get the numerator?

  41. anonymous
    • 5 years ago
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    I just multiplied (a-b) by the LCD: ab and got (a-b)ab

  42. smurfy14
    • 5 years ago
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    oh duh lol so would you simplify that farther?

  43. anonymous
    • 5 years ago
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    Yes, at this point the equation looks like [(a-b)ab]/(b-a) and if we factor out -1 from the denominator we get [(a-b)ab]/[-(a-b)]

  44. anonymous
    • 5 years ago
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    Then the (a-b) cancels and we get -ab

  45. smurfy14
    • 5 years ago
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    oh ok thank you soo much!!

  46. anonymous
    • 5 years ago
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    No problem, glad I could help! :)

  47. anonymous
    • 5 years ago
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    \[\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x^2}+\frac{1}{y^2}+\frac{2}{x y}}=\frac{\frac{-x^2+y^2}{x^2 y^2}}{\frac{x^2+2 x y+y^2}{x^2 y^2}}=\frac{-x^2+y^2}{x^2+2 x y+y^2}=\frac{(-(x-y) )}{(x+y)}=\frac{-x+y}{x+y}\]\[1-\frac{2 x}{x+y}=\frac{-x+y}{x+y} \]

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