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anonymous

  • one year ago

How to simplify this?? \[ \frac{-\sqrt{3} - 1}{1+(-\sqrt{3})*1}\] \[ \frac{-\sqrt{3} - 1}{1-\sqrt{3}}\] \[ \frac{-\sqrt{3} - 1}{1-\sqrt{3}} * \frac{1-\sqrt{3}} {1-\sqrt{3}} \] \[ \frac{2}{2(2-\sqrt{3})} \] Is this correct??

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  1. anonymous
    • one year ago
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    In step 3, you should multiply the expression by the denominator's conjugate, top and bottom.

  2. anonymous
    • one year ago
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    That allows you to eliminate radical expressions in the denominator.

  3. anonymous
    • one year ago
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    Could you show me? I don't see what you mean. I thought I did multiply the expression

  4. anonymous
    • one year ago
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    \[\frac{ -\sqrt{3}-1 }{ 1-\sqrt{3} } \times \frac{ 1+\sqrt{3} }{ 1+\sqrt{3} } \]

  5. anonymous
    • one year ago
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    That should be your step 3.

  6. anonymous
    • one year ago
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    I did that and I get 2 for the numerator and \( 2(2-\sqrt{3})\) for the denominator

  7. anonymous
    • one year ago
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    No, if you multiply a radical expression by its conjugate, the square roots disappear.

  8. anonymous
    • one year ago
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    Yeah, I used the same I see that.

  9. anonymous
    • one year ago
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    I use - and not the conjugate

  10. anonymous
    • one year ago
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    \[(1-\sqrt{3})(1+\sqrt{3}) = 1-\sqrt{3} + \sqrt{3} - 3 = 2\]

  11. anonymous
    • one year ago
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    Do you agree with my above expansion?

  12. anonymous
    • one year ago
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    Yes

  13. anonymous
    • one year ago
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    Ok, so 2 is now your denominator.

  14. anonymous
    • one year ago
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    Let me do the top

  15. anonymous
    • one year ago
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    Let's multiply the numerator now.

  16. anonymous
    • one year ago
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    I got -2

  17. anonymous
    • one year ago
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    One sec I made a boo boo

  18. anonymous
    • one year ago
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    Check your numerator again. It should contain some square roots.

  19. anonymous
    • one year ago
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    I have \[ -\sqrt{3} -\sqrt{9} -1 -\sqrt{3} \] is this correct?

  20. anonymous
    • one year ago
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    Yes, you can combine the terms to make it easier to read.

  21. anonymous
    • one year ago
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    \[-2\sqrt{3}-4\]

  22. anonymous
    • one year ago
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    Now that you have the numerator, don't forget that you still have a denominator, -2.

  23. anonymous
    • one year ago
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    From what I put up where di the 4 come from?

  24. anonymous
    • one year ago
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    Oh your \[- \sqrt{9} - 1 = -3 - 1 = - 4\]

  25. anonymous
    • one year ago
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    Combine your numerator and your denominator, now what do you have?

  26. anonymous
    • one year ago
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    Ok how about eh 2 and the sqr(3) ?? from what I put up.

  27. anonymous
    • one year ago
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    Oh that's from \[-\sqrt{3}-\sqrt{3} = -2\sqrt{3}\]

  28. anonymous
    • one year ago
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    \[\frac{ -2\sqrt{3}-4 }{ -2 } = \sqrt{3} + 2\]

  29. anonymous
    • one year ago
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    Yep that is it. Thank you so much.

  30. anonymous
    • one year ago
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    Are you a qualified helper?

  31. anonymous
    • one year ago
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    I just like to help :)

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