(2/(3x-4))-1/20=5/(6x-8)

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Solution for (2/(3x-4))-1/20=5/(6x-8) equation: 


D( x )

3*x-4 = 0

6*x-8 = 0

3*x-4 = 0

3*x-4 = 0

3*x-4 = 0 // + 4

3*x = 4 // : 3

x = 4/3

6*x-8 = 0

6*x-8 = 0

6*x-8 = 0 // + 8

6*x = 8 // : 6

x = 8/6

x = 4/3

x in (-oo:4/3) U (4/3:+oo)

2/(3*x-4)-(1/20) = 5/(6*x-8) // - 5/(6*x-8)

2/(3*x-4)-(5/(6*x-8))-(1/20) = 0

2/(3*x-4)-5*(6*x-8)^-1-1/20 = 0

2/(3*x-4)-5/(6*x-8)-1/20 = 0

(2*20*(6*x-8))/(20*(3*x-4)*(6*x-8))+(-5*20*(3*x-4))/(20*(3*x-4)*(6*x-8))+(-1*(3*x-4)*(6*x-8))/(20*(3*x-4)*(6*x-8)) = 0

2*20*(6*x-8)-5*20*(3*x-4)-1*(3*x-4)*(6*x-8) = 0

48*x-18*x^2-60*x-32+80 = 0

48-18*x^2-12*x = 0

48-18*x^2-12*x = 0

6*(8-3*x^2-2*x) = 0

8-3*x^2-2*x = 0

DELTA = (-2)^2-(-3*4*8)

DELTA = 100

DELTA > 0

x = (100^(1/2)+2)/(-3*2) or x = (2-100^(1/2))/(-3*2)

x = -2 or x = 4/3

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

(6*(x+2)*(x-4/3))/(20*(3*x-4)*(6*x-8)) = 0

(6*(x+2)*(x-4/3))/(20*(3*x-4)*(6*x-8)) = 0 // * 20*(3*x-4)*(6*x-8)

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

( 6 )

6 = 0

x belongs to the empty set

( x+2 )

x+2 = 0 // - 2

x = -2

( x-4/3 )

x-4/3 = 0 // + 4/3

x = 4/3

x in { 4/3} 

x = -2

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