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