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How would I solve the following equation for x: 1/(1-sqrtx)=1-(sqrtx)/(sqrtx-1)
\[\frac{-1}{\sqrt{x}-1}=\frac{\sqrt{x}-1-\sqrt{x}}{\sqrt{x}-1}\]
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
why did you add a negative sqrtx to the left? and I am trying to solve for x, not prove that it is true.
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
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.
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.
Okay, I guess I was thinking that I had to isolate x and get an actual value. But thank you!!
wait, on the right, where did the extra sqrtx come from?
Had to rewrite the number 1 as: \[\frac{\sqrt{x}-1}{\sqrt{x}-1}\]
so where did the extra sqrtx come from, though?
ahhh, okay! thanks again!