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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-2x+2x*x-7=0

Wy multiply elements

2x^2-2x-7=0

a = 2; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·2·(-7)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{15}}{2*2}=\frac{2-2\sqrt{15}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{15}}{2*2}=\frac{2+2\sqrt{15}}{4}
$