2x+6/x-5=x+3/x-1

Solution for 2x+6/x-5=x+3/x-1 equation:

2x+6/x-5=x+3/x-1

We move all terms to the left:

2x+6/x-5-(x+3/x-1)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

2x+6/x-x-3/x+1-5=0

We multiply all the terms by the denominator


2x*x-x*x+1*x-5*x+6-3=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

x^2-4x+3=0

a = 1; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·1·3
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{-(-4)-2}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2*1}=\frac{6}{2}
=3
$