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5x-8/x-1=4/x
We move all terms to the left:
5x-8/x-1-(4/x)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5x-8/x-(+4/x)-1=0
We get rid of parentheses
5x-8/x-4/x-1=0
We multiply all the terms by the denominator
5x*x-1*x-8-4=0
We add all the numbers together, and all the variables
-1x+5x*x-12=0
Wy multiply elements
5x^2-1x-12=0
a = 5; b = -1; c = -12;
Δ = b2-4ac
Δ = -12-4·5·(-12)
Δ = 241
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{-(-1)-\sqrt{241}}{2*5}=\frac{1-\sqrt{241}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{241}}{2*5}=\frac{1+\sqrt{241}}{10} $
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