(6x-7)/(1-5x)=(x-3)/(x-9)

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Solution for (6x-7)/(1-5x)=(x-3)/(x-9) equation:


D( x )

1-(5*x) = 0

x-9 = 0

1-(5*x) = 0

1-(5*x) = 0

1-5*x = 0

1-5*x = 0 // - 1

-5*x = -1 // : -5

x = -1/(-5)

x = 1/5

x-9 = 0

x-9 = 0

x-9 = 0 // + 9

x = 9

x in (-oo:1/5) U (1/5:9) U (9:+oo)

(6*x-7)/(1-(5*x)) = (x-3)/(x-9) // - (x-3)/(x-9)

(6*x-7)/(1-(5*x))-((x-3)/(x-9)) = 0

(6*x-7)/(1-5*x)-((x-3)/(x-9)) = 0

(6*x-7)/(1-5*x)+(-1*(x-3))/(x-9) = 0

((6*x-7)*(x-9))/((1-5*x)*(x-9))+(-1*(x-3)*(1-5*x))/((1-5*x)*(x-9)) = 0

(6*x-7)*(x-9)-1*(x-3)*(1-5*x) = 0

11*x^2-77*x+66 = 0

11*x^2-77*x+66 = 0

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

x^2-7*x+6 = 0

DELTA = (-7)^2-(1*4*6)

DELTA = 25

DELTA > 0

x = (25^(1/2)+7)/(1*2) or x = (7-25^(1/2))/(1*2)

x = 6 or x = 1

11*(x-1)*(x-6) = 0

(11*(x-1)*(x-6))/((1-5*x)*(x-9)) = 0

(11*(x-1)*(x-6))/((1-5*x)*(x-9)) = 0 // * (1-5*x)*(x-9)

11*(x-1)*(x-6) = 0

( x-1 )

x-1 = 0 // + 1

x = 1

( x-6 )

x-6 = 0 // + 6

x = 6

x in { 1, 6 }

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