2r-4/(r-2)

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Solution for 2r-4/(r-2) equation: 


D( r )

r-2 = 0

r-2 = 0

r-2 = 0

r-2 = 0 // + 2

r = 2

r in (-oo:2) U (2:+oo)

2*r-(4/(r-2)) = 0

2*r-4*(r-2)^-1 = 0

2*r-4/(r-2) = 0

(2*r*(r-2))/(r-2)-4/(r-2) = 0

2*r*(r-2)-4 = 0

2*r^2-4*r-4 = 0

2*r^2-4*r-4 = 0

2*(r^2-2*r-2) = 0

r^2-2*r-2 = 0

DELTA = (-2)^2-(-2*1*4)

DELTA = 12

DELTA > 0

r = (12^(1/2)+2)/(1*2) or r = (2-12^(1/2))/(1*2)

r = (2*3^(1/2)+2)/2 or r = (2-2*3^(1/2))/2

2*(r-((2-2*3^(1/2))/2))*(r-((2*3^(1/2)+2)/2)) = 0

(2*(r-((2-2*3^(1/2))/2))*(r-((2*3^(1/2)+2)/2)))/(r-2) = 0

(2*(r-((2-2*3^(1/2))/2))*(r-((2*3^(1/2)+2)/2)))/(r-2) = 0 // * r-2

2*(r-((2-2*3^(1/2))/2))*(r-((2*3^(1/2)+2)/2)) = 0

( r-((2*3^(1/2)+2)/2) )

r-((2*3^(1/2)+2)/2) = 0 // + (2*3^(1/2)+2)/2

r = (2*3^(1/2)+2)/2

( r-((2-2*3^(1/2))/2) )

r-((2-2*3^(1/2))/2) = 0 // + (2-2*3^(1/2))/2

r = (2-2*3^(1/2))/2

r in { (2*3^(1/2)+2)/2, (2-2*3^(1/2))/2 }

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