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3/x-1=4/4+x
We move all terms to the left:
3/x-1-(4/4+x)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 4+x)!=0We add all the numbers together, and all the variables
We move all terms containing x to the left, all other terms to the right
x)!=-4
x!=-4/1
x!=-4
x∈R
3/x-(x+1)-1=0
We get rid of parentheses
3/x-x-1-1=0
We multiply all the terms by the denominator
-x*x-1*x-1*x+3=0
We add all the numbers together, and all the variables
-2x-x*x+3=0
Wy multiply elements
-1x^2-2x+3=0
a = -1; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-1)·3
Δ = 16
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{16}=4$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*-1}=\frac{-2}{-2} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*-1}=\frac{6}{-2} =-3 $
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