1/x+1+1=x+2

Solution for 1/x+1+1=x+2 equation:

1/x+1+1=x+2

We move all terms to the left:

1/x+1+1-(x+2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1/x-(x+2)+2=0

We get rid of parentheses

1/x-x-2+2=0

We multiply all the terms by the denominator


-x*x-2*x+2*x+1=0

We add all the numbers together, and all the variables

-x*x+1=0

Wy multiply elements

-1x^2+1=0

a = -1; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-1)·1
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2}{2*-1}=\frac{2}{-2}
=-1
$