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qwerter

  • 3 years ago

How would I solve the following equation for x: 1/(1-sqrtx)=1-(sqrtx)/(sqrtx-1)

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  1. qwerter
    • 3 years ago
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    |dw:1359341309231:dw|

  2. Mertsj
    • 3 years ago
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    \[\frac{-1}{\sqrt{x}-1}=\frac{\sqrt{x}-1-\sqrt{x}}{\sqrt{x}-1}\]

  3. Mertsj
    • 3 years ago
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    So we see that the left side and the right side are identical so the equation is true of all values of x that are greater than or equal to 0

  4. qwerter
    • 3 years ago
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    why did you add a negative sqrtx to the left? and I am trying to solve for x, not prove that it is true.

  5. Mertsj
    • 3 years ago
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    I wanted the denominator on the left to be the same as the denominator on the right so I multiplied numerator and denominator by -1

  6. qwerter
    • 3 years ago
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    makes sense

  7. Mertsj
    • 3 years ago
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    And I did solve for x. x is all real numbers greater than or equal to 0. Just because there are many solutions does not mean the problem is not solved.

  8. Mertsj
    • 3 years ago
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    It's sort of like if you have to solve an equation such as: x+3 = x+3 That is true for all real numbers.

  9. qwerter
    • 3 years ago
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    Okay, I guess I was thinking that I had to isolate x and get an actual value. But thank you!!

  10. Mertsj
    • 3 years ago
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    yw

  11. qwerter
    • 3 years ago
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    wait, on the right, where did the extra sqrtx come from?

  12. Mertsj
    • 3 years ago
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    Had to rewrite the number 1 as: \[\frac{\sqrt{x}-1}{\sqrt{x}-1}\]

  13. qwerter
    • 3 years ago
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    so where did the extra sqrtx come from, though?

  14. Mertsj
    • 3 years ago
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    |dw:1359342501576:dw|

  15. qwerter
    • 3 years ago
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    ahhh, okay! thanks again!

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