x-1/1-6/x-1=1

Solution for x-1/1-6/x-1=1 equation:

x-1/1-6/x-1=1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


determiningTheFunctionDomain
x-6/x-1-1-1/1=0

We add all the numbers together, and all the variables

x-6/x-3=0

We multiply all the terms by the denominator


x*x-3*x-6=0

We add all the numbers together, and all the variables

-3x+x*x-6=0

Wy multiply elements

x^2-3x-6=0

a = 1; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·1·(-6)
Δ = 33
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{-(-3)-\sqrt{33}}{2*1}=\frac{3-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*1}=\frac{3+\sqrt{33}}{2}
$