(3x-2)/(1-4x)=(x-3)/(x+5)

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Solution for (3x-2)/(1-4x)=(x-3)/(x+5) equation:


D( x )

x+5 = 0

1-(4*x) = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

1-(4*x) = 0

1-(4*x) = 0

1-4*x = 0

1-4*x = 0 // - 1

-4*x = -1 // : -4

x = -1/(-4)

x = 1/4

x in (-oo:-5) U (-5:1/4) U (1/4:+oo)

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

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

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

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

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

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

7*x^2-7 = 0

(7*x^2-7)/((1-4*x)*(x+5)) = 0

(7*x^2-7)/((1-4*x)*(x+5)) = 0 // * (1-4*x)*(x+5)

7*x^2-7 = 0

7*x^2 = 7 // : 7

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

x in { 1, -1 }

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