x/(x-4)+4/(x+1)=(19x-1)/(x^2-3x-4)

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Solution for x/(x-4)+4/(x+1)=(19x-1)/(x^2-3x-4) equation:


D( x )

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

x+1 = 0

x-4 = 0

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

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

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

x = 4 or x = -1

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

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

x/(x-4)+4/(x+1) = (19*x-1)/(x^2-(3*x)-4) // - (19*x-1)/(x^2-(3*x)-4)

x/(x-4)+4/(x+1)-((19*x-1)/(x^2-(3*x)-4)) = 0

x/(x-4)+4/(x+1)-((19*x-1)/(x^2-3*x-4)) = 0

x/(x-4)+4/(x+1)+(-1*(19*x-1))/(x^2-3*x-4) = 0

x^2-3*x-4 = 0

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

x = 4 or x = -1

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

x/(x-4)+4/(x+1)+(-1*(19*x-1))/((x+1)*(x-4)) = 0

(x*(x+1))/((x-4)*(x+1))+(4*(x-4))/((x-4)*(x+1))+(-1*(19*x-1))/((x-4)*(x+1)) = 0

x*(x+1)+4*(x-4)-1*(19*x-1) = 0

x^2+5*x-19*x-16+1 = 0

x^2-14*x-15 = 0

x^2-14*x-15 = 0

x^2-14*x-15 = 0

DELTA = (-14)^2-(-15*1*4)

DELTA = 256

DELTA > 0

x = (256^(1/2)+14)/(1*2) or x = (14-256^(1/2))/(1*2)

x = 15 or x = -1

(x+1)*(x-15) = 0

((x+1)*(x-15))/((x-4)*(x+1)) = 0

((x+1)*(x-15))/((x-4)*(x+1)) = 0 // * (x-4)*(x+1)

(x+1)*(x-15) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-15 )

x-15 = 0 // + 15

x = 15

x in { -1}

x = 15

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