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

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


D( x )

x+3 = 0

x^2+2*x-3 = 0

x-1 = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

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-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

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

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

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

(x+1)/(x-1)+3/(x+3)-8/(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+3)*(x-1) = 0

(x+1)/(x-1)+3/(x+3)-8/((x+3)*(x-1)) = 0

((x+1)*(x+3))/((x-1)*(x+3))+(3*(x-1))/((x-1)*(x+3))-8/((x-1)*(x+3)) = 0

(x+1)*(x+3)+3*(x-1)-8 = 0

x^2+7*x-8 = 0

x^2+7*x-8 = 0

x^2+7*x-8 = 0

DELTA = 7^2-(-8*1*4)

DELTA = 81

DELTA > 0

x = (81^(1/2)-7)/(1*2) or x = (-81^(1/2)-7)/(1*2)

x = 1 or x = -8

(x+8)*(x-1) = 0

((x+8)*(x-1))/((x-1)*(x+3)) = 0

((x+8)*(x-1))/((x-1)*(x+3)) = 0 // * (x-1)*(x+3)

(x+8)*(x-1) = 0

( x+8 )

x+8 = 0 // - 8

x = -8

( x-1 )

x-1 = 0 // + 1

x = 1

x in { 1} 

x = -8

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