(7x-6)/(1-4x)=(x-4)/(x+8)

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Solution for (7x-6)/(1-4x)=(x-4)/(x+8) equation:


D( x )

1-(4*x) = 0

x+8 = 0

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+8 = 0

x+8 = 0

x+8 = 0 // - 8

x = -8

x in (-oo:-8) U (-8:1/4) U (1/4:+oo)

(7*x-6)/(1-(4*x)) = (x-4)/(x+8) // - (x-4)/(x+8)

(7*x-6)/(1-(4*x))-((x-4)/(x+8)) = 0

(7*x-6)/(1-4*x)-((x-4)/(x+8)) = 0

(7*x-6)/(1-4*x)+(-1*(x-4))/(x+8) = 0

((7*x-6)*(x+8))/((1-4*x)*(x+8))+(-1*(x-4)*(1-4*x))/((1-4*x)*(x+8)) = 0

(7*x-6)*(x+8)-1*(x-4)*(1-4*x) = 0

11*x^2+33*x-44 = 0

11*x^2+33*x-44 = 0

11*(x^2+3*x-4) = 0

x^2+3*x-4 = 0

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

DELTA = 25

DELTA > 0

x = (25^(1/2)-3)/(1*2) or x = (-25^(1/2)-3)/(1*2)

x = 1 or x = -4

11*(x+4)*(x-1) = 0

(11*(x+4)*(x-1))/((1-4*x)*(x+8)) = 0

(11*(x+4)*(x-1))/((1-4*x)*(x+8)) = 0 // * (1-4*x)*(x+8)

11*(x+4)*(x-1) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -4, 1 }

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