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3/x-3=5/2x+1
We move all terms to the left:
3/x-3-(5/2x+1)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 2x+1)!=0We get rid of parentheses
x∈R
3/x-5/2x-1-3=0
We calculate fractions
6x/2x^2+(-5x)/2x^2-1-3=0
We add all the numbers together, and all the variables
6x/2x^2+(-5x)/2x^2-4=0
We multiply all the terms by the denominator
6x+(-5x)-4*2x^2=0
Wy multiply elements
-8x^2+6x+(-5x)=0
We get rid of parentheses
-8x^2+6x-5x=0
We add all the numbers together, and all the variables
-8x^2+x=0
a = -8; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-8)·0
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-8}=\frac{-2}{-16} =1/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-8}=\frac{0}{-16} =0 $
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