(3x-1)/(2x-3)-(x+9)/(4x-6)=1

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Solution for (3x-1)/(2x-3)-(x+9)/(4x-6)=1 equation:


D( x )

4*x-6 = 0

2*x-3 = 0

4*x-6 = 0

4*x-6 = 0

4*x-6 = 0 // + 6

4*x = 6 // : 4

x = 6/4

x = 3/2

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0 // + 3

2*x = 3 // : 2

x = 3/2

x in (-oo:3/2) U (3/2:+oo)

(3*x-1)/(2*x-3)-((x+9)/(4*x-6)) = 1 // - 1

(3*x-1)/(2*x-3)-((x+9)/(4*x-6))-1 = 0

(3*x-1)/(2*x-3)+(-1*(x+9))/(4*x-6)-1 = 0

((3*x-1)*(4*x-6))/((2*x-3)*(4*x-6))+(-1*(x+9)*(2*x-3))/((2*x-3)*(4*x-6))+(-1*(2*x-3)*(4*x-6))/((2*x-3)*(4*x-6)) = 0

(3*x-1)*(4*x-6)-1*(x+9)*(2*x-3)-1*(2*x-3)*(4*x-6) = 0

10*x^2-8*x^2-37*x+24*x-18+33 = 0

2*x^2-13*x+15 = 0

2*x^2-13*x+15 = 0

2*x^2-13*x+15 = 0

DELTA = (-13)^2-(2*4*15)

DELTA = 49

DELTA > 0

x = (49^(1/2)+13)/(2*2) or x = (13-49^(1/2))/(2*2)

x = 5 or x = 3/2

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

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

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

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

( x-3/2 )

x-3/2 = 0 // + 3/2

x = 3/2

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 3/2}

x = 5

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