6/x-1-4/x-3=8/2x-6

Solution for 6/x-1-4/x-3=8/2x-6 equation:

6/x-1-4/x-3=8/2x-6

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-6)!=0

x∈R


We add all the numbers together, and all the variables

6/x-4/x-(8/2x-6)-4=0

We get rid of parentheses

6/x-4/x-8/2x+6-4=0

We calculate fractions


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

We add all the numbers together, and all the variables

(-8x+6)/2x^2+(-8x)/2x^2+2=0

We multiply all the terms by the denominator


(-8x+6)+(-8x)+2*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-16x+6=0

a = 4; b = -16; c = +6;
Δ = b2-4ac
Δ = -162-4·4·6
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{10}}{2*4}=\frac{16-4\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{10}}{2*4}=\frac{16+4\sqrt{10}}{8}
$