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

Solution for 3/x+1-4/2-x=0 equation:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/x-1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -1; b = -1; c = +3;
Δ = b2-4ac
Δ = -12-4·(-1)·3
Δ = 13
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{13}}{2*-1}=\frac{1-\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{13}}{2*-1}=\frac{1+\sqrt{13}}{-2}
$