x+4/x-1-5=1/x-1

Solution for x+4/x-1-5=1/x-1 equation:

x+4/x-1-5=1/x-1

We move all terms to the left:

x+4/x-1-5-(1/x-1)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

x+4/x-(1/x-1)-6=0

We get rid of parentheses

x+4/x-1/x+1-6=0

We multiply all the terms by the denominator


x*x+1*x-6*x+4-1=0

We add all the numbers together, and all the variables

-5x+x*x+3=0

Wy multiply elements

x^2-5x+3=0

a = 1; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·1·3
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{13}}{2*1}=\frac{5-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*1}=\frac{5+\sqrt{13}}{2}
$