4x-1/x+1=x-1

Solution for 4x-1/x+1=x-1 equation:

4x-1/x+1=x-1

We move all terms to the left:

4x-1/x+1-(x-1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

3x^2+2x-1=0

a = 3; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·3·(-1)
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{-(2)-4}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4}{2*3}=\frac{2}{6}
=1/3
$