(w)/(w-1)-(5w)/(5w-2)=(w-2)/(5w-7w+2)

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Solution for (w)/(w-1)-(5w)/(5w-2)=(w-2)/(5w-7w+2) equation:


D( w )

5*w-2 = 0

5*w-(7*w)+2 = 0

w-1 = 0

5*w-2 = 0

5*w-2 = 0

5*w-2 = 0 // + 2

5*w = 2 // : 5

w = 2/5

5*w-(7*w)+2 = 0

5*w-(7*w)+2 = 0

5*w-7*w+2 = 0

2-2*w = 0 // - 2

-2*w = -2 // : -2

w = -2/(-2)

w = 1

w-1 = 0

w-1 = 0

w-1 = 0 // + 1

w = 1

w in (-oo:2/5) U (2/5:1) U (1:+oo)

w/(w-1)-((5*w)/(5*w-2)) = (w-2)/(5*w-(7*w)+2) // - (w-2)/(5*w-(7*w)+2)

w/(w-1)-((5*w)/(5*w-2))-((w-2)/(5*w-(7*w)+2)) = 0

w/(w-1)-5*w*(5*w-2)^-1-((w-2)/(5*w-7*w+2)) = 0

w/(w-1)+(-5*w)/(5*w-2)+(-1*(w-2))/(2-2*w) = 0

(w*(5*w-2)*(2-2*w))/((w-1)*(5*w-2)*(2-2*w))+(-5*w*(w-1)*(2-2*w))/((w-1)*(5*w-2)*(2-2*w))+(-1*(w-2)*(w-1)*(5*w-2))/((w-1)*(5*w-2)*(2-2*w)) = 0

w*(5*w-2)*(2-2*w)-5*w*(w-1)*(2-2*w)-1*(w-2)*(w-1)*(5*w-2) = 0

17*w^2-5*w^3-6*w^2+6*w-16*w+4 = 0

11*w^2-5*w^3-10*w+4 = 0

11*w^2-5*w^3-10*w+4 = 0

11*w^2-5*w^3-10*w+4 = 0

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

1

w = 1

11*w^2-5*w^3-10*w+4 = 0

1

w-1

6*w-5*w^2-4

11*w^2-5*w^3-10*w+4

w-1

5*w^3-5*w^2

6*w^2-10*w+4

6*w-6*w^2

4-4*w

4*w-4

0

6*w-5*w^2-4 = 0

DELTA = 6^2-(-5*(-4)*4)

DELTA = -44

DELTA < 0

w in { 1}

w-1 = 0

(w-1)/((w-1)*(5*w-2)*(2-2*w)) = 0

(w-1)/((w-1)*(5*w-2)*(2-2*w)) = 0 // * (w-1)*(5*w-2)*(2-2*w)

w-1 = 0

w-1 = 0 // + 1

w = 1

w in { 1}

w belongs to the empty set

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