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(3/x+1)-1/2=1/3x+3
We move all terms to the left:
(3/x+1)-1/2-(1/3x+3)=0
Domain of the equation: x+1)!=0
x∈R
Domain of the equation: 3x+3)!=0We get rid of parentheses
x∈R
3/x-1/3x+1-3-1/2=0
We calculate fractions
(-9x^2)/12x^2+36x/12x^2+(-4x)/12x^2+1-3=0
We add all the numbers together, and all the variables
(-9x^2)/12x^2+36x/12x^2+(-4x)/12x^2-2=0
We multiply all the terms by the denominator
(-9x^2)+36x+(-4x)-2*12x^2=0
Wy multiply elements
(-9x^2)-24x^2+36x+(-4x)=0
We get rid of parentheses
-9x^2-24x^2+36x-4x=0
We add all the numbers together, and all the variables
-33x^2+32x=0
a = -33; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-33)·0
Δ = 1024
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{1024}=32$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-33}=\frac{-64}{-66} =32/33 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-33}=\frac{0}{-66} =0 $
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