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

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Solution for (((4-4x)/(x^2+2x-3))+x)=0 equation: 


D( x )

x^2+2*x-3 = 0

x^2+2*x-3 = 0

x^2+2*x-3 = 0

x^2+2*x-3 = 0

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

DELTA = 16

DELTA > 0

x = (16^(1/2)-2)/(1*2) or x = (-16^(1/2)-2)/(1*2)

x = 1 or x = -3

x in (-oo:-3) U (-3:1) U (1:+oo)

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

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

x^2+2*x-3 = 0

x^2+2*x-3 = 0

x^2+2*x-3 = 0

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

DELTA = 16

DELTA > 0

x = (16^(1/2)-2)/(1*2) or x = (-16^(1/2)-2)/(1*2)

x = 1 or x = -3

(x+3)*(x-1) = 0

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

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

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

x^3+2*x^2-7*x+4 = 0

x^3+2*x^2-7*x+4 = 0

x^3+2*x^2-7*x+4 = 0

{ 1, -1, 2, -2, 4, -4 }

1

x = 1

x^3+2*x^2-7*x+4 = 0

1

x-1

x^2+3*x-4

x^3+2*x^2-7*x+4

x-1

x^2-x^3

3*x^2-7*x+4

3*x-3*x^2

4-4*x

4*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

x in { -4, 1, 1} 

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

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

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

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

( x+4 )

x+4 = 0 // - 4

x = -4

( x-1 )

x-1 = 0 // + 1

x = 1

x in { 1} 

x = -4

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