(x-1)/(x+1)-1/3x=(3x-5)/(4x+4)

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


D( x )

x+1 = 0

4*x+4 = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

4*x+4 = 0

4*x+4 = 0

4*x+4 = 0 // - 4

4*x = -4 // : 4

x = -4/4

x = -1

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

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

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

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

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

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

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

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

2*x-4*x^3-5*x^2+3 = 0

2*x-4*x^3-5*x^2+3 = 0

2*x-4*x^3-5*x^2+3 = 0

{ 1, -1, 3, -3 }

1

x = 1

2*x-4*x^3-5*x^2+3 = -4

1

-1

x = -1

2*x-4*x^3-5*x^2+3 = 0

-1

x+1

3-4*x^2-x

2*x-4*x^3-5*x^2+3

x+1

4*x^3+4*x^2

2*x-x^2+3

x^2+x

3*x+3

-3*x-3

0

3-4*x^2-x = 0

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

DELTA = 49

DELTA > 0

x = (49^(1/2)+1)/(-4*2) or x = (1-49^(1/2))/(-4*2)

x = -1 or x = 3/4

x in { -1, 3/4, -1}

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

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

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x-3/4 )

x-3/4 = 0 // + 3/4

x = 3/4

x in { -1}

x = 3/4

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