((x+3)/(x-1))+((x+4)/(x+1))=((8x+5)/((x^2)-1))

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Solution for ((x+3)/(x-1))+((x+4)/(x+1))=((8x+5)/((x^2)-1)) equation: 


D( x )

x^2-1 = 0

x+1 = 0

x-1 = 0

x^2-1 = 0

x^2-1 = 0

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

(x+3)/(x-1)+(x+4)/(x+1) = (8*x+5)/(x^2-1) // - (8*x+5)/(x^2-1)

(x+3)/(x-1)+(x+4)/(x+1)-((8*x+5)/(x^2-1)) = 0

(x+3)/(x-1)+(x+4)/(x+1)+(-1*(8*x+5))/(x^2-1) = 0

((x+3)*(x+1)*(x^2-1))/((x-1)*(x+1)*(x^2-1))+((x+4)*(x-1)*(x^2-1))/((x-1)*(x+1)*(x^2-1))+(-1*(8*x+5)*(x-1)*(x+1))/((x-1)*(x+1)*(x^2-1)) = 0

(x+3)*(x+1)*(x^2-1)+(x+4)*(x-1)*(x^2-1)-1*(8*x+5)*(x-1)*(x+1) = 0

2*x^4+7*x^3-8*x^3-3*x^2-5*x^2-7*x+8*x+1+5 = 0

2*x^4-x^3-8*x^2+x+6 = 0

2*x^4-x^3-8*x^2+x+6 = 0

2*x^4-x^3-8*x^2+x+6 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6 }

1

x = 1

2*x^4-x^3-8*x^2+x+6 = 0

1

x-1

2*x^3+x^2-7*x-6

2*x^4-x^3-8*x^2+x+6

x-1

2*x^3-2*x^4

x^3-8*x^2+x+6

x^2-x^3

x-7*x^2+6

7*x^2-7*x

6-6*x

6*x-6

0

2*x^3+x^2-7*x-6 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6 }

1

x = 1

2*x^3+x^2-7*x-6 = -10

1

-1

x = -1

2*x^3+x^2-7*x-6 = 0

-1

x+1

2*x^2-x-6

2*x^3+x^2-7*x-6

x+1

-2*x^3-2*x^2

-x^2-7*x-6

x^2+x

-6*x-6

6*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

x in { -3/2, 2, 1, -1} 

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

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

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x+3/2 )

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

x = -3/2

( x-1 )

x-1 = 0 // + 1

x = 1

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -1} 

x in { 1} 

x in { -3/2, 2 }

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