x+1-2/x1-1/x=x+2

Solution for x+1-2/x1-1/x=x+2 equation:

x+1-2/x1-1/x=x+2

We move all terms to the left:

x+1-2/x1-1/x-(x+2)=0


Domain of the equation: x1!=0

x^1!=0/

x^1!=√0

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We get rid of parentheses

x-2/x1-1/x-x-2+1=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


(-2x)+(-1x)-1*x^2=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-3x=0

a = -1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-1)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-1}=\frac{6}{-2}
=-3
$