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2x+3/x+1=5x-6/x+1
We move all terms to the left:
2x+3/x+1-(5x-6/x+1)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: x+1)!=0We get rid of parentheses
x∈R
2x+3/x-5x+6/x-1+1=0
We multiply all the terms by the denominator
2x*x-5x*x-1*x+1*x+3+6=0
We add all the numbers together, and all the variables
2x*x-5x*x+9=0
Wy multiply elements
2x^2-5x^2+9=0
We add all the numbers together, and all the variables
-3x^2+9=0
a = -3; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-3)·9
Δ = 108
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{3}}{2*-3}=\frac{0-6\sqrt{3}}{-6} =-\frac{6\sqrt{3}}{-6} =-\frac{\sqrt{3}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{3}}{2*-3}=\frac{0+6\sqrt{3}}{-6} =\frac{6\sqrt{3}}{-6} =\frac{\sqrt{3}}{-1} $
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