## qwerter 2 years ago How would I solve the following equation for x: 1/(1-sqrtx)=1-(sqrtx)/(sqrtx-1)

1. qwerter

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2. Mertsj

$\frac{-1}{\sqrt{x}-1}=\frac{\sqrt{x}-1-\sqrt{x}}{\sqrt{x}-1}$

3. Mertsj

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

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

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

makes sense

7. Mertsj

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

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

Okay, I guess I was thinking that I had to isolate x and get an actual value. But thank you!!

10. Mertsj

yw

11. qwerter

wait, on the right, where did the extra sqrtx come from?

12. Mertsj

Had to rewrite the number 1 as: $\frac{\sqrt{x}-1}{\sqrt{x}-1}$

13. qwerter

so where did the extra sqrtx come from, though?

14. Mertsj

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15. qwerter

ahhh, okay! thanks again!