7/(2u-6)+1=-4/(u-3)

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Solution for 7/(2u-6)+1=-4/(u-3) equation: 


D( u )

u-3 = 0

2*u-6 = 0

u-3 = 0

u-3 = 0

u-3 = 0 // + 3

u = 3

2*u-6 = 0

2*u-6 = 0

2*u-6 = 0 // + 6

2*u = 6 // : 2

u = 6/2

u = 3

u in (-oo:3) U (3:+oo)

7/(2*u-6)+1 = -4/(u-3) // + -4/(u-3)

7/(2*u-6)-(-4/(u-3))+1 = 0

7/(2*u-6)+4*(u-3)^-1+1 = 0

7/(2*u-6)+4/(u-3)+1 = 0

(7*(u-3))/((2*u-6)*(u-3))+(4*(2*u-6))/((2*u-6)*(u-3))+(1*(2*u-6)*(u-3))/((2*u-6)*(u-3)) = 0

7*(u-3)+4*(2*u-6)+1*(2*u-6)*(u-3) = 0

2*u^2+15*u-12*u-45+18 = 0

2*u^2+3*u-27 = 0

2*u^2+3*u-27 = 0

2*u^2+3*u-27 = 0

DELTA = 3^2-(-27*2*4)

DELTA = 225

DELTA > 0

u = (225^(1/2)-3)/(2*2) or u = (-225^(1/2)-3)/(2*2)

u = 3 or u = -9/2

(u+9/2)*(u-3) = 0

((u+9/2)*(u-3))/((2*u-6)*(u-3)) = 0

((u+9/2)*(u-3))/((2*u-6)*(u-3)) = 0 // * (2*u-6)*(u-3)

(u+9/2)*(u-3) = 0

( u+9/2 )

u+9/2 = 0 // - 9/2

u = -9/2

( u-3 )

u-3 = 0 // + 3

u = 3

u in { 3} 

u = -9/2

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