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1/x+3-1/6x+18=x/x+1
We move all terms to the left:
1/x+3-1/6x+18-(x/x+1)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: x+1)!=0We add all the numbers together, and all the variables
x∈R
1/x-1/6x-(x/x+1)+21=0
We get rid of parentheses
1/x-1/6x-x/x-1+21=0
Fractions to decimals
1/x-1/6x-1+21+1=0
We calculate fractions
6x/6x^2+(-x)/6x^2-1+21+1=0
We add all the numbers together, and all the variables
6x/6x^2+(-1x)/6x^2-1+21+1=0
We add all the numbers together, and all the variables
6x/6x^2+(-1x)/6x^2+21=0
We multiply all the terms by the denominator
6x+(-1x)+21*6x^2=0
Wy multiply elements
126x^2+6x+(-1x)=0
We get rid of parentheses
126x^2+6x-1x=0
We add all the numbers together, and all the variables
126x^2+5x=0
a = 126; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·126·0
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*126}=\frac{-10}{252} =-5/126 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*126}=\frac{0}{252} =0 $
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