2x-3/x-1=4x-5/x-1

Solution for 2x-3/x-1=4x-5/x-1 equation:

2x-3/x-1=4x-5/x-1

We move all terms to the left:

2x-3/x-1-(4x-5/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-3/x-4x+5/x+1-1=0

We multiply all the terms by the denominator


2x*x-4x*x+1*x-1*x-3+5=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-2x^2+2=0

a = -2; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-2)·2
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-2}=\frac{4}{-4}
=-1
$