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6/6x+4=2/x-4
We move all terms to the left:
6/6x+4-(2/x-4)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: x-4)!=0We get rid of parentheses
x∈R
6/6x-2/x+4+4=0
We calculate fractions
6x/6x^2+(-12x)/6x^2+4+4=0
We add all the numbers together, and all the variables
6x/6x^2+(-12x)/6x^2+8=0
We multiply all the terms by the denominator
6x+(-12x)+8*6x^2=0
Wy multiply elements
48x^2+6x+(-12x)=0
We get rid of parentheses
48x^2+6x-12x=0
We add all the numbers together, and all the variables
48x^2-6x=0
a = 48; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·48·0
Δ = 36
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*48}=\frac{0}{96} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*48}=\frac{12}{96} =1/8 $
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