x-3/x-2+1=-x-2/x-4

Solution for x-3/x-2+1=-x-2/x-4 equation:

x-3/x-2+1=-x-2/x-4

We move all terms to the left:

x-3/x-2+1-(-x-2/x-4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We add all the numbers together, and all the variables

x-3/x-(-1x-2/x-4)-2+1=0

We add all the numbers together, and all the variables

x-3/x-(-1x-2/x-4)-1=0

We get rid of parentheses

x-3/x+1x+2/x+4-1=0

We multiply all the terms by the denominator


x*x+1x*x+4*x-1*x-3+2=0

We add all the numbers together, and all the variables

3x+x*x+1x*x-1=0

Wy multiply elements

x^2+x^2+3x-1=0

We add all the numbers together, and all the variables

2x^2+3x-1=0

a = 2; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·2·(-1)
Δ = 17
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{-(3)-\sqrt{17}}{2*2}=\frac{-3-\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{17}}{2*2}=\frac{-3+\sqrt{17}}{4}
$