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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x-3-3x-1)!=0

We move all terms containing x to the left, all other terms to the right

x-3x-1)!=3

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

3/x-2/x-(-3x+4/x-4)-5=0

We get rid of parentheses

3/x-2/x+3x-4/x+4-5=0

We multiply all the terms by the denominator


3x*x+4*x-5*x+3-2-4=0

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2-1x-3=0

a = 3; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·3·(-3)
Δ = 37
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{37}}{2*3}=\frac{1-\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{37}}{2*3}=\frac{1+\sqrt{37}}{6}
$