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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: (x-2)!=0

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

x!=2

x∈R


We calculate fractions


(3x-6)/(x^2-2x)+(-x)/(x^2-2x)-4=0

We add all the numbers together, and all the variables

(3x-6)/(x^2-2x)+(-1x)/(x^2-2x)-4=0

We multiply all the terms by the denominator


(3x-6)+(-1x)-4*(x^2-2x)=0

We multiply parentheses

-4x^2+(3x-6)+(-1x)+8x=0

We get rid of parentheses

-4x^2+3x-1x+8x-6=0

We add all the numbers together, and all the variables

-4x^2+10x-6=0

a = -4; b = 10; c = -6;
Δ = b2-4ac
Δ = 102-4·(-4)·(-6)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*-4}=\frac{-12}{-8}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*-4}=\frac{-8}{-8}
=1
$