(5x-6)/(1-6x)=(x+1)/(x+9)

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


D( x )

1-(6*x) = 0

x+9 = 0

1-(6*x) = 0

1-(6*x) = 0

1-6*x = 0

1-6*x = 0 // - 1

-6*x = -1 // : -6

x = -1/(-6)

x = 1/6

x+9 = 0

x+9 = 0

x+9 = 0 // - 9

x = -9

x in (-oo:-9) U (-9:1/6) U (1/6:+oo)

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

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

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

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

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

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

11*x^2+44*x-55 = 0

11*x^2+44*x-55 = 0

11*(x^2+4*x-5) = 0

x^2+4*x-5 = 0

DELTA = 4^2-(-5*1*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)-4)/(1*2) or x = (-36^(1/2)-4)/(1*2)

x = 1 or x = -5

11*(x+5)*(x-1) = 0

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

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

11*(x+5)*(x-1) = 0

( x+5 )

x+5 = 0 // - 5

x = -5

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -5, 1 }

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