2/(x-4)=(-5)/(3x-12)+4

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Solution for 2/(x-4)=(-5)/(3x-12)+4 equation: 


D( x )

x-4 = 0

3*x-12 = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

3*x-12 = 0

3*x-12 = 0

3*x-12 = 0 // + 12

3*x = 12 // : 3

x = 12/3

x = 4

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

2/(x-4) = 4-5/(3*x-12) // - 4-5/(3*x-12)

2/(x-4)-(-5/(3*x-12))-4 = 0

2/(x-4)+5*(3*x-12)^-1-4 = 0

2/(x-4)+5/(3*x-12)-4 = 0

(2*(3*x-12))/((x-4)*(3*x-12))+(5*(x-4))/((x-4)*(3*x-12))+(-4*(x-4)*(3*x-12))/((x-4)*(3*x-12)) = 0

2*(3*x-12)+5*(x-4)-4*(x-4)*(3*x-12) = 0

11*x-12*x^2+96*x-192-44 = 0

107*x-12*x^2-236 = 0

107*x-12*x^2-236 = 0

107*x-12*x^2-236 = 0

DELTA = 107^2-(-236*(-12)*4)

DELTA = 121

DELTA > 0

x = (121^(1/2)-107)/(-12*2) or x = (-121^(1/2)-107)/(-12*2)

x = 4 or x = 59/12

(x-4)*(x-59/12) = 0

((x-4)*(x-59/12))/((x-4)*(3*x-12)) = 0

((x-4)*(x-59/12))/((x-4)*(3*x-12)) = 0 // * (x-4)*(3*x-12)

(x-4)*(x-59/12) = 0

( x-4 )

x-4 = 0 // + 4

x = 4

( x-59/12 )

x-59/12 = 0 // + 59/12

x = 59/12

x in { 4} 

x = 59/12

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