## qwerter Group Title How would I solve the following equation for x: 1/(1-sqrtx)=1-(sqrtx)/(sqrtx-1) one year ago one year ago

1. qwerter Group Title

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2. Mertsj Group Title

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

3. Mertsj Group Title

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 Group Title

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 Group Title

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 Group Title

makes sense

7. Mertsj Group Title

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 Group Title

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 Group Title

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

10. Mertsj Group Title

yw

11. qwerter Group Title

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

12. Mertsj Group Title

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

13. qwerter Group Title

so where did the extra sqrtx come from, though?

14. Mertsj Group Title

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15. qwerter Group Title

ahhh, okay! thanks again!