w/(w-5)-(3w)/(3w-5)=(w-2)/(3w^2-20w+25)

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Solution for w/(w-5)-(3w)/(3w-5)=(w-2)/(3w^2-20w+25) equation: 


D( w )

3*w^2-(20*w)+25 = 0

3*w-5 = 0

w-5 = 0

3*w^2-(20*w)+25 = 0

3*w^2-(20*w)+25 = 0

3*w^2-20*w+25 = 0

3*w^2-20*w+25 = 0

DELTA = (-20)^2-(3*4*25)

DELTA = 100

DELTA > 0

w = (100^(1/2)+20)/(2*3) or w = (20-100^(1/2))/(2*3)

w = 5 or w = 5/3

3*w-5 = 0

3*w-5 = 0

3*w-5 = 0 // + 5

3*w = 5 // : 3

w = 5/3

w-5 = 0

w-5 = 0

w-5 = 0 // + 5

w = 5

w in (-oo:5/3) U (5/3:5) U (5:+oo)

w/(w-5)-((3*w)/(3*w-5)) = (w-2)/(3*w^2-(20*w)+25) // - (w-2)/(3*w^2-(20*w)+25)

w/(w-5)-((3*w)/(3*w-5))-((w-2)/(3*w^2-(20*w)+25)) = 0

w/(w-5)-3*w*(3*w-5)^-1-((w-2)/(3*w^2-20*w+25)) = 0

w/(w-5)+(-3*w)/(3*w-5)+(-1*(w-2))/(3*w^2-20*w+25) = 0

3*w^2-20*w+25 = 0

3*w^2-20*w+25 = 0

3*w^2-20*w+25 = 0

DELTA = (-20)^2-(3*4*25)

DELTA = 100

DELTA > 0

w = (100^(1/2)+20)/(2*3) or w = (20-100^(1/2))/(2*3)

w = 5 or w = 5/3

(w-5/3)*(w-5) = 0

w/(w-5)+(-3*w)/(3*w-5)+(-1*(w-2))/((w-5/3)*(w-5)) = 0

(w*(3*w-5)*(w-5/3))/((w-5)*(3*w-5)*(w-5/3))+(-3*w*(w-5)*(w-5/3))/((w-5)*(3*w-5)*(w-5/3))+(-1*(w-2)*(3*w-5))/((w-5)*(3*w-5)*(w-5/3)) = 0

w*(3*w-5)*(w-5/3)-3*w*(w-5)*(w-5/3)-1*(w-2)*(3*w-5) = 0

10*w^2-3*w^2-50/3*w+11*w-10 = 0

7*w^2-17/3*w-10 = 0

7*w^2-17/3*w-10 = 0

7*w^2-17/3*w-10 = 0

DELTA = (-17/3)^2-(-10*4*7)

DELTA = 2809/9

DELTA > 0

w = ((2809/9)^(1/2)+17/3)/(2*7) or w = (17/3-(2809/9)^(1/2))/(2*7)

w = 5/3 or w = -6/7

(w+6/7)*(w-5/3) = 0

((w+6/7)*(w-5/3))/((w-5)*(3*w-5)*(w-5/3)) = 0

((w+6/7)*(w-5/3))/((w-5)*(3*w-5)*(w-5/3)) = 0 // * (w-5)*(3*w-5)*(w-5/3)

(w+6/7)*(w-5/3) = 0

( w+6/7 )

w+6/7 = 0 // - 6/7

w = -6/7

( w-5/3 )

w-5/3 = 0 // + 5/3

w = 5/3

w in { 5/3} 

w = -6/7

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