(5x-4)/(1-5x)=(x+16)/(x-9)

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Solution for (5x-4)/(1-5x)=(x+16)/(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)

(5*x-4)/(1-(5*x)) = (x+16)/(x-9) // - (x+16)/(x-9)

(5*x-4)/(1-(5*x))-((x+16)/(x-9)) = 0

(5*x-4)/(1-5*x)-((x+16)/(x-9)) = 0

(5*x-4)/(1-5*x)+(-1*(x+16))/(x-9) = 0

((5*x-4)*(x-9))/((1-5*x)*(x-9))+(-1*(x+16)*(1-5*x))/((1-5*x)*(x-9)) = 0

(5*x-4)*(x-9)-1*(x+16)*(1-5*x) = 0

10*x^2+30*x+20 = 0

10*x^2+30*x+20 = 0

10*(x^2+3*x+2) = 0

x^2+3*x+2 = 0

DELTA = 3^2-(1*2*4)

DELTA = 1

DELTA > 0

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

x = -1 or x = -2

10*(x+2)*(x+1) = 0

(10*(x+2)*(x+1))/((1-5*x)*(x-9)) = 0

(10*(x+2)*(x+1))/((1-5*x)*(x-9)) = 0 // * (1-5*x)*(x-9)

10*(x+2)*(x+1) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x+2 )

x+2 = 0 // - 2

x = -2

x in { -1, -2 }

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