((6x)/(x+4))+4=((2x+2)/(x-1))

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Solution for ((6x)/(x+4))+4=((2x+2)/(x-1)) equation: 


D( x )

x+4 = 0

x-1 = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

(6*x)/(x+4)+4 = (2*x+2)/(x-1) // - (2*x+2)/(x-1)

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

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

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

6*x*(x-1)-1*(2*x+2)*(x+4)+4*(x+4)*(x-1) = 0

4*x^2+4*x^2-16*x+12*x-16-8 = 0

8*x^2-4*x-24 = 0

8*x^2-4*x-24 = 0

4*(2*x^2-x-6) = 0

2*x^2-x-6 = 0

DELTA = (-1)^2-(-6*2*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+1)/(2*2) or x = (1-49^(1/2))/(2*2)

x = 2 or x = -3/2

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

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

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

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

( x+3/2 )

x+3/2 = 0 // - 3/2

x = -3/2

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -3/2, 2 }

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