2/(b-2)=b/(b^2-3b+2)+b/(2b-2)

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Solution for 2/(b-2)=b/(b^2-3b+2)+b/(2b-2) equation:


D( b )

2*b-2 = 0

b-2 = 0

b^2-(3*b)+2 = 0

2*b-2 = 0

2*b-2 = 0

2*b-2 = 0 // + 2

2*b = 2 // : 2

b = 2/2

b = 1

b-2 = 0

b-2 = 0

b-2 = 0 // + 2

b = 2

b^2-(3*b)+2 = 0

b^2-(3*b)+2 = 0

b^2-3*b+2 = 0

b^2-3*b+2 = 0

DELTA = (-3)^2-(1*2*4)

DELTA = 1

DELTA > 0

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

b = 2 or b = 1

b in (-oo:1) U (1:2) U (2:+oo)

2/(b-2) = b/(b^2-(3*b)+2)+b/(2*b-2) // - b/(b^2-(3*b)+2)+b/(2*b-2)

2/(b-2)-(b/(b^2-(3*b)+2))-(b/(2*b-2)) = 0

2/(b-2)-(b/(b^2-3*b+2))-(b/(2*b-2)) = 0

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

b^2-3*b+2 = 0

b^2-3*b+2 = 0

b^2-3*b+2 = 0

DELTA = (-3)^2-(1*2*4)

DELTA = 1

DELTA > 0

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

b = 2 or b = 1

(b-1)*(b-2) = 0

2/(b-2)+(-1*b)/((b-1)*(b-2))+(-1*b)/(2*b-2) = 0

(2*(b-1)*(2*b-2))/((b-2)*(b-1)*(2*b-2))+(-1*b*(2*b-2))/((b-2)*(b-1)*(2*b-2))+(-1*b*(b-2)*(b-1))/((b-2)*(b-1)*(2*b-2)) = 0

2*(b-1)*(2*b-2)-1*b*(2*b-2)-1*b*(b-2)*(b-1) = 0

2*b^2-b^3+3*b^2-6*b-2*b+4 = 0

5*b^2-b^3-8*b+4 = 0

5*b^2-b^3-8*b+4 = 0

5*b^2-b^3-8*b+4 = 0

{ 1, -1, 2, -2, 4, -4 }

1

b = 1

5*b^2-b^3-8*b+4 = 0

1

b-1

4*b-b^2-4

5*b^2-b^3-8*b+4

b-1

b^3-b^2

4*b^2-8*b+4

4*b-4*b^2

4-4*b

4*b-4

0

4*b-b^2-4 = 0

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

DELTA = 0

b = -4/(-1*2)

b = 2 or b = 2

b in { 2, 2, 1}

(b-2)^2*(b-1) = 0

((b-2)^2*(b-1))/((b-2)*(b-1)*(2*b-2)) = 0

((b-2)^2*(b-1))/((b-2)*(b-1)*(2*b-2)) = 0 // * (b-2)*(b-1)*(2*b-2)

(b-2)^2*(b-1) = 0

( b-1 )

b-1 = 0 // + 1

b = 1

( b-2 )

b-2 = 0 // + 2

b = 2

b in { 1}

b in { 2}

b belongs to the empty set

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