(4x+1)/(x+1)=(12)/(x^2-1)

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Solution for (4x+1)/(x+1)=(12)/(x^2-1) equation: 


D( x )

x^2-1 = 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 in (-oo:-1) U (-1:1) U (1:+oo)

(4*x+1)/(x+1) = 12/(x^2-1) // - 12/(x^2-1)

(4*x+1)/(x+1)-(12/(x^2-1)) = 0

(4*x+1)/(x+1)-12*(x^2-1)^-1 = 0

(4*x+1)/(x+1)-12/(x^2-1) = 0

((4*x+1)*(x^2-1))/((x+1)*(x^2-1))+(-12*(x+1))/((x+1)*(x^2-1)) = 0

(4*x+1)*(x^2-1)-12*(x+1) = 0

4*x^3+x^2-16*x-13 = 0

4*x^3+x^2-16*x-13 = 0

4*x^3+x^2-16*x-13 = 0

{ 1, -1, 13, -13 }

1

x = 1

4*x^3+x^2-16*x-13 = -24

1

-1

x = -1

4*x^3+x^2-16*x-13 = 0

-1

x+1

4*x^2-3*x-13

4*x^3+x^2-16*x-13

x+1

-4*x^3-4*x^2

-3*x^2-16*x-13

3*x^2+3*x

-13*x-13

13*x+13

0

4*x^2-3*x-13 = 0

DELTA = (-3)^2-(-13*4*4)

DELTA = 217

DELTA > 0

x = (217^(1/2)+3)/(2*4) or x = (3-217^(1/2))/(2*4)

x = (217^(1/2)+3)/8 or x = (3-217^(1/2))/8

x in { (3-217^(1/2))/8, (217^(1/2)+3)/8, -1} 

(x-((3-217^(1/2))/8))*(x-((217^(1/2)+3)/8))*(x+1) = 0

((x-((3-217^(1/2))/8))*(x-((217^(1/2)+3)/8))*(x+1))/((x+1)*(x^2-1)) = 0

((x-((3-217^(1/2))/8))*(x-((217^(1/2)+3)/8))*(x+1))/((x+1)*(x^2-1)) = 0 // * (x+1)*(x^2-1)

(x-((3-217^(1/2))/8))*(x-((217^(1/2)+3)/8))*(x+1) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-((217^(1/2)+3)/8) )

x-((217^(1/2)+3)/8) = 0 // + (217^(1/2)+3)/8

x = (217^(1/2)+3)/8

( x-((3-217^(1/2))/8) )

x-((3-217^(1/2))/8) = 0 // + (3-217^(1/2))/8

x = (3-217^(1/2))/8

x in { -1} 

x in { (217^(1/2)+3)/8, (3-217^(1/2))/8 }

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