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3x-3/x-1=2
We move all terms to the left:
3x-3/x-1-(2)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
3x-3/x-3=0
We multiply all the terms by the denominator
3x*x-3*x-3=0
We add all the numbers together, and all the variables
-3x+3x*x-3=0
Wy multiply elements
3x^2-3x-3=0
a = 3; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·3·(-3)
Δ = 45
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{5}}{2*3}=\frac{3-3\sqrt{5}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{5}}{2*3}=\frac{3+3\sqrt{5}}{6} $
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