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anonymous

  • one year ago

Help please

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  1. anonymous
    • one year ago
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    |dw:1441001669103:dw|

  2. anonymous
    • one year ago
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    simplifying radical expressions

  3. jim_thompson5910
    • one year ago
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    does it want you to apply a limit? or just simplify?

  4. anonymous
    • one year ago
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    just simplify

  5. jim_thompson5910
    • one year ago
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    ok like before, multiply top and bottom by \(\Large \sqrt{x+h}+\sqrt{x}\) \[\Large \frac{\sqrt{x+h}-\sqrt{x}}{h}\] \[\Large \frac{(\sqrt{x+h}-\sqrt{x})}{h}\times \color{red}{\frac{(\sqrt{x+h}+\sqrt{x})}{(\sqrt{x+h}+\sqrt{x})}}\]

  6. jim_thompson5910
    • one year ago
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    tell me what you get in the numerator after multiplying

  7. anonymous
    • one year ago
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    why isn't it multiplied by the bottom?

  8. jim_thompson5910
    • one year ago
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    it is. I multiplied both top and bottom

  9. jim_thompson5910
    • one year ago
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    |dw:1441002457520:dw|

  10. anonymous
    • one year ago
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    is it |dw:1441002458990:dw|

  11. jim_thompson5910
    • one year ago
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    the 2x+2h is incorrect

  12. anonymous
    • one year ago
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    |dw:1441002630632:dw|

  13. jim_thompson5910
    • one year ago
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    Yes you're on the right track. One more step and you'll get `h` as the simplified result in the numerator \[\Large (\color{red}{a}-\color{blue}{b})(\color{red}{a}+\color{blue}{b}) = \color{red}{a}^2 - \color{blue}{b}^2\] \[\Large (\color{red}{\sqrt{x+h}}-\color{blue}{\sqrt{x}})(\color{red}{\sqrt{x+h}}+\color{blue}{\sqrt{x}}) = (\color{red}{\sqrt{x+h}})^2 - (\color{blue}{\sqrt{x}})^2\] \[\Large (\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}) = x+h - x\] \[\Large (\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}) = h\]

  14. jim_thompson5910
    • one year ago
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    so we'll have \[\Large \frac{x+h-x}{h(\sqrt{x+h}+\sqrt{x})}\] \[\Large \frac{h}{h(\sqrt{x+h}+\sqrt{x})}\] \[\Large \frac{\cancel{h}}{\cancel{h}(\sqrt{x+h}+\sqrt{x})}\] \[\Large \frac{1}{\sqrt{x+h}+\sqrt{x}}\]

  15. anonymous
    • one year ago
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    i'm going to try solving one on my own and can you check it to see if i'm doing it correctly?

  16. jim_thompson5910
    • one year ago
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    sure that sounds like a good plan

  17. anonymous
    • one year ago
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    would this be correct|dw:1441003416350:dw|

  18. jim_thompson5910
    • one year ago
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    your steps and final answer are correct

  19. anonymous
    • one year ago
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    alright thanks and could you help me with one last problem because i'm lost on it

  20. jim_thompson5910
    • one year ago
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    sure

  21. anonymous
    • one year ago
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    |dw:1441003887720:dw|

  22. jim_thompson5910
    • one year ago
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    I'm guessing it wants you to rationalize the denominator?

  23. anonymous
    • one year ago
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    i think so

  24. jim_thompson5910
    • one year ago
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    then multiply top and bottom by the conjugate of the denominator

  25. anonymous
    • one year ago
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    it doesn't specify all it says is simplify the radical expression

  26. jim_thompson5910
    • one year ago
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    |dw:1441004360029:dw|

  27. anonymous
    • one year ago
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    |dw:1441004288227:dw|

  28. jim_thompson5910
    • one year ago
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    the denominator is correct but the numerator is not

  29. jim_thompson5910
    • one year ago
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    you should have |dw:1441004582602:dw|

  30. jim_thompson5910
    • one year ago
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    you have to FOIL it all out

  31. anonymous
    • one year ago
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    |dw:1441004525342:dw|

  32. jim_thompson5910
    • one year ago
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    correct

  33. anonymous
    • one year ago
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    well bye have a good night and thank you very much for all your help i really appreciate it

  34. jim_thompson5910
    • one year ago
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    you're welcome and good night

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