(7)/(w^2-5w+6)=(1)/(w-3)+(5)/(w-2)

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Solution for (7)/(w^2-5w+6)=(1)/(w-3)+(5)/(w-2) equation: 


D( w )

w^2-(5*w)+6 = 0

w-3 = 0

w-2 = 0

w^2-(5*w)+6 = 0

w^2-(5*w)+6 = 0

w^2-5*w+6 = 0

w^2-5*w+6 = 0

DELTA = (-5)^2-(1*4*6)

DELTA = 1

DELTA > 0

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

w = 3 or w = 2

w-3 = 0

w-3 = 0

w-3 = 0 // + 3

w = 3

w-2 = 0

w-2 = 0

w-2 = 0 // + 2

w = 2

w in (-oo:2) U (2:3) U (3:+oo)

7/(w^2-(5*w)+6) = 1/(w-3)+5/(w-2) // - 1/(w-3)+5/(w-2)

7/(w^2-(5*w)+6)-(1/(w-3))-(5/(w-2)) = 0

7/(w^2-5*w+6)-(w-3)^-1-5*(w-2)^-1 = 0

7/(w^2-5*w+6)-1/(w-3)-5/(w-2) = 0

w^2-5*w+6 = 0

w^2-5*w+6 = 0

w^2-5*w+6 = 0

DELTA = (-5)^2-(1*4*6)

DELTA = 1

DELTA > 0

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

w = 3 or w = 2

(w-2)*(w-3) = 0

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

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

7-1*(w-2)-5*(w-3) = 0

9-w-5*w+15 = 0

24-6*w = 0

(24-6*w)/((w-2)*(w-3)) = 0

(24-6*w)/((w-2)*(w-3)) = 0 // * (w-2)*(w-3)

24-6*w = 0

24-6*w = 0 // - 24

-6*w = -24 // : -6

w = -24/(-6)

w = 4

w = 4

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