1/1-(1-x)=1/x

Solution for 1/1-(1-x)=1/x equation:

1/1-(1-x)=1/x

We move all terms to the left:

1/1-(1-x)-(1/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(-1x+1)-(+1/x)+1/1=0

We add all the numbers together, and all the variables

-(-1x+1)-(+1/x)=0

We get rid of parentheses

1x-1/x-1=0

We multiply all the terms by the denominator


1x*x-1*x-1=0

We add all the numbers together, and all the variables

-1x+1x*x-1=0

Wy multiply elements

x^2-1x-1=0

a = 1; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·1·(-1)
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{5}}{2*1}=\frac{1-\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{5}}{2*1}=\frac{1+\sqrt{5}}{2}
$