2/(x-3)=-7/(4x-12)+2

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Solution for 2/(x-3)=-7/(4x-12)+2 equation: 


D( x )

4*x-12 = 0

x-3 = 0

4*x-12 = 0

4*x-12 = 0

4*x-12 = 0 // + 12

4*x = 12 // : 4

x = 12/4

x = 3

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

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

2/(x-3) = 2-7/(4*x-12) // - 2-7/(4*x-12)

2/(x-3)-(-7/(4*x-12))-2 = 0

2/(x-3)+7*(4*x-12)^-1-2 = 0

2/(x-3)+7/(4*x-12)-2 = 0

(2*(4*x-12))/((x-3)*(4*x-12))+(7*(x-3))/((x-3)*(4*x-12))+(-2*(x-3)*(4*x-12))/((x-3)*(4*x-12)) = 0

2*(4*x-12)+7*(x-3)-2*(x-3)*(4*x-12) = 0

15*x-8*x^2+48*x-72-45 = 0

63*x-8*x^2-117 = 0

63*x-8*x^2-117 = 0

63*x-8*x^2-117 = 0

DELTA = 63^2-(-117*(-8)*4)

DELTA = 225

DELTA > 0

x = (225^(1/2)-63)/(-8*2) or x = (-225^(1/2)-63)/(-8*2)

x = 3 or x = 39/8

(x-3)*(x-39/8) = 0

((x-3)*(x-39/8))/((x-3)*(4*x-12)) = 0

((x-3)*(x-39/8))/((x-3)*(4*x-12)) = 0 // * (x-3)*(4*x-12)

(x-3)*(x-39/8) = 0

( x-3 )

x-3 = 0 // + 3

x = 3

( x-39/8 )

x-39/8 = 0 // + 39/8

x = 39/8

x in { 3} 

x = 39/8

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