3/x-2/x-1=1/2x

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

3/x-2/x-1=1/2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


(-4x+3)+(-1x)-1*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-5x+3=0

a = -2; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·(-2)·3
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*-2}=\frac{12}{-4}
=-3
$