x/(x^2+3x-4)+(x+1)/(x^2+6x+8)=2x/(x^2+x-2)

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Solution for x/(x^2+3x-4)+(x+1)/(x^2+6x+8)=2x/(x^2+x-2) equation: 


D( x )

x^2+x-2 = 0

x^2+6*x+8 = 0

x^2+3*x-4 = 0

x^2+x-2 = 0

x^2+x-2 = 0

x^2+x-2 = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)-1)/(1*2) or x = (-9^(1/2)-1)/(1*2)

x = 1 or x = -2

x^2+6*x+8 = 0

x^2+6*x+8 = 0

x^2+6*x+8 = 0

DELTA = 6^2-(1*4*8)

DELTA = 4

DELTA > 0

x = (4^(1/2)-6)/(1*2) or x = (-4^(1/2)-6)/(1*2)

x = -2 or x = -4

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

x = 1 or x = -4

x in (-oo:-4) U (-4:-2) U (-2:1) U (1:+oo)

x/(x^2+3*x-4)+(x+1)/(x^2+6*x+8) = (2*x)/(x^2+x-2) // - (2*x)/(x^2+x-2)

x/(x^2+3*x-4)+(x+1)/(x^2+6*x+8)-((2*x)/(x^2+x-2)) = 0

x/(x^2+3*x-4)+(x+1)/(x^2+6*x+8)-2*x*(x^2+x-2)^-1 = 0

x/(x^2+3*x-4)+(x+1)/(x^2+6*x+8)+(-2*x)/(x^2+x-2) = 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 = (-25^(1/2)-3)/(1*2)

x = 1 or x = -4

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

x^2+6*x+8 = 0

x^2+6*x+8 = 0

x^2+6*x+8 = 0

DELTA = 6^2-(1*4*8)

DELTA = 4

DELTA > 0

x = (4^(1/2)-6)/(1*2) or x = (-4^(1/2)-6)/(1*2)

x = -2 or x = -4

(x+4)*(x+2) = 0

x^2+x-2 = 0

x^2+x-2 = 0

x^2+x-2 = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)-1)/(1*2) or x = (-9^(1/2)-1)/(1*2)

x = 1 or x = -2

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

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

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

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

2*x^2-2*x^2+2*x-8*x-1 = 0

-6*x-1 = 0

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

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

-6*x-1 = 0

-6*x-1 = 0 // + 1

-6*x = 1 // : -6

x = 1/(-6)

x = -1/6

x = -1/6

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