w/(w-5)-(5w)/(5w-4)=(w-1)/((5w-4)(w-25))

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Solution for w/(w-5)-(5w)/(5w-4)=(w-1)/((5w-4)(w-25)) equation: 


D( w )

(5*w-4)*(w-25) = 0

5*w-4 = 0

w-5 = 0

(5*w-4)*(w-25) = 0

(5*w-4)*(w-25) = 0

( 5*w-4 )

5*w-4 = 0 // + 4

5*w = 4 // : 5

w = 4/5

( w-25 )

w-25 = 0 // + 25

w = 25

5*w-4 = 0

5*w-4 = 0

5*w-4 = 0 // + 4

5*w = 4 // : 5

w = 4/5

w-5 = 0

w-5 = 0

w-5 = 0 // + 5

w = 5

w in (-oo:4/5) U (4/5:5) U (5:25) U (25:+oo)

w/(w-5)-((5*w)/(5*w-4)) = (w-1)/((5*w-4)*(w-25)) // - (w-1)/((5*w-4)*(w-25))

w/(w-5)-((5*w)/(5*w-4))-((w-1)/((5*w-4)*(w-25))) = 0

w/(w-5)-5*w*(5*w-4)^-1-((w-1)/((5*w-4)*(w-25))) = 0

w/(w-5)+(-5*w)/(5*w-4)+(-1*(w-1))/((5*w-4)*(w-25)) = 0

(w*(5*w-4))/((w-5)*(5*w-4))+(-5*w*(w-5))/((w-5)*(5*w-4))+(-1*(w-1)*(w-5))/((w-5)*(5*w-4)) = 0

w*(5*w-4)-5*w*(w-5)-1*(w-1)*(w-5) = 0

21*w-w^2+6*w-5 = 0

27*w-w^2-5 = 0

27*w-w^2-5 = 0

27*w-w^2-5 = 0

DELTA = 27^2-(-5*(-1)*4)

DELTA = 709

DELTA > 0

w = (709^(1/2)-27)/(-1*2) or w = (-709^(1/2)-27)/(-1*2)

w = (709^(1/2)-27)/(-2) or w = (709^(1/2)+27)/2

(w-((709^(1/2)-27)/(-2)))*(w-((709^(1/2)+27)/2)) = 0

((w-((709^(1/2)-27)/(-2)))*(w-((709^(1/2)+27)/2)))/((w-5)*(5*w-4)) = 0

((w-((709^(1/2)-27)/(-2)))*(w-((709^(1/2)+27)/2)))/((w-5)*(5*w-4)) = 0 // * (w-5)*(5*w-4)

(w-((709^(1/2)-27)/(-2)))*(w-((709^(1/2)+27)/2)) = 0

( w-((709^(1/2)+27)/2) )

w-((709^(1/2)+27)/2) = 0 // + (709^(1/2)+27)/2

w = (709^(1/2)+27)/2

( w-((709^(1/2)-27)/(-2)) )

w-((709^(1/2)-27)/(-2)) = 0 // + (709^(1/2)-27)/(-2)

w = (709^(1/2)-27)/(-2)

w in { (709^(1/2)+27)/2, (709^(1/2)-27)/(-2) }

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