(-7/(5w-20))+1=(3/(w-4))

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Solution for (-7/(5w-20))+1=(3/(w-4)) equation: 


D( w )

5*w-20 = 0

w-4 = 0

5*w-20 = 0

5*w-20 = 0

5*w-20 = 0 // + 20

5*w = 20 // : 5

w = 20/5

w = 4

w-4 = 0

w-4 = 0

w-4 = 0 // + 4

w = 4

w in (-oo:4) U (4:+oo)

1-7/(5*w-20) = 3/(w-4) // - 3/(w-4)

1-7/(5*w-20)-(3/(w-4)) = 0

1-7/(5*w-20)-3*(w-4)^-1 = 0

1-7/(5*w-20)-3/(w-4) = 0

(-7*(w-4))/((5*w-20)*(w-4))+(-3*(5*w-20))/((5*w-20)*(w-4))+(1*(5*w-20)*(w-4))/((5*w-20)*(w-4)) = 0

1*(5*w-20)*(w-4)-7*(w-4)-3*(5*w-20) = 0

5*w^2-22*w-40*w+80+88 = 0

5*w^2-62*w+168 = 0

5*w^2-62*w+168 = 0

5*w^2-62*w+168 = 0

DELTA = (-62)^2-(4*5*168)

DELTA = 484

DELTA > 0

w = (484^(1/2)+62)/(2*5) or w = (62-484^(1/2))/(2*5)

w = 42/5 or w = 4

(w-4)*(w-42/5) = 0

((w-4)*(w-42/5))/((5*w-20)*(w-4)) = 0

((w-4)*(w-42/5))/((5*w-20)*(w-4)) = 0 // * (5*w-20)*(w-4)

(w-4)*(w-42/5) = 0

( w-4 )

w-4 = 0 // + 4

w = 4

( w-42/5 )

w-42/5 = 0 // + 42/5

w = 42/5

w in { 4} 

w = 42/5

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