(3x-5)/(2x-6)-(4x-2)/(5x-15)

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Solution for (3x-5)/(2x-6)-(4x-2)/(5x-15) equation:


D( x )

5*x-15 = 0

2*x-6 = 0

5*x-15 = 0

5*x-15 = 0

5*x-15 = 0 // + 15

5*x = 15 // : 5

x = 15/5

x = 3

2*x-6 = 0

2*x-6 = 0

2*x-6 = 0 // + 6

2*x = 6 // : 2

x = 6/2

x = 3

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

(3*x-5)/(2*x-6)-((4*x-2)/(5*x-15)) = 0

(3*x-5)/(2*x-6)+(-1*(4*x-2))/(5*x-15) = 0

((3*x-5)*(5*x-15))/((2*x-6)*(5*x-15))+(-1*(4*x-2)*(2*x-6))/((2*x-6)*(5*x-15)) = 0

(3*x-5)*(5*x-15)-1*(4*x-2)*(2*x-6) = 0

7*x^2-42*x+63 = 0

7*x^2-42*x+63 = 0

7*(x^2-6*x+9) = 0

x^2-6*x+9 = 0

DELTA = (-6)^2-(1*4*9)

DELTA = 0

x = 6/(1*2)

x = 3 or x = 3

7*(x-3)^2 = 0

(7*(x-3)^2)/((2*x-6)*(5*x-15)) = 0

(7*(x-3)^2)/((2*x-6)*(5*x-15)) = 0 // * (2*x-6)*(5*x-15)

7*(x-3)^2 = 0

x-3 = 0 // + 3

x = 3

x in { 3}

x belongs to the empty set

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