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anonymous

  • one year ago

Rationalize the numerator:

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  1. anonymous
    • one year ago
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    \[(\sqrt{x} - \sqrt{x+h}) / h \]

  2. freckles
    • one year ago
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    multiply top and bottom by conjugate of top

  3. anonymous
    • one year ago
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    I understand how to do it. You get -1 for the top, but not sure of the bottom.

  4. freckles
    • one year ago
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    \[\frac{\sqrt{x}-\sqrt{x+h}}{h} \cdot \frac{\sqrt{x}+\sqrt{x+h}}{\sqrt{x}+\sqrt{x+h}}\]

  5. freckles
    • one year ago
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    you get -1 on top before or after canceling common factors after the multiplication part

  6. freckles
    • one year ago
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    and that was a question

  7. anonymous
    • one year ago
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    I know the answer for the bottom is \[\sqrt{x} + \sqrt{x+h}\] but how do you get that with the multiplied h?

  8. freckles
    • one year ago
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    \[\frac{(x)-(x+h)}{h(\sqrt{x}+\sqrt{x+h})}\] you do understand we have -h/h=-1 right?

  9. anonymous
    • one year ago
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    Yes

  10. freckles
    • one year ago
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    so what is the question exactly

  11. anonymous
    • one year ago
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    How does it work out for the bottom?

  12. freckles
    • one year ago
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    after using -h/h=-1 you are left with sqrt(x)+sqrt(x+h) there is nothing else to do unless you have a limit question here

  13. freckles
    • one year ago
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    sqrt(x)+sqrt(x+h) on the bottom*

  14. freckles
    • one year ago
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    \[\frac{(x)-(x+h)}{h(\sqrt{x}+\sqrt{x+h})}=\frac{-h}{h} \frac{1}{\sqrt{x}+\sqrt{x+h}}\]

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