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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!=0determiningTheFunctionDomain x-6/x-1-1-1/1=0
x∈R
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} $
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