1+1/x=x/x+1x

Solution for 1+1/x=x/x+1x equation:

1+1/x=x/x+1x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+1x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/x-x-x/x+1=0

Fractions to decimals

1/x-x+1+1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x-x*x+1=0

Wy multiply elements

-1x^2+2x+1=0

a = -1; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-1)·1
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{2}}{2*-1}=\frac{-2-2\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{2}}{2*-1}=\frac{-2+2\sqrt{2}}{-2}
$