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

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


D( x )

2*x-2 = 0

x+1 = 0

x-1 = 0

2*x-2 = 0

2*x-2 = 0

2*x-2 = 0 // + 2

2*x = 2 // : 2

x = 2/2

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)

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

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

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

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

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

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

13*x^2-8*x^2-20*x+7+8 = 0

5*x^2-20*x+15 = 0

5*x^2-20*x+15 = 0

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

x^2-4*x+3 = 0

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

DELTA = 4

DELTA > 0

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

x = 3 or x = 1

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

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

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

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

( x-1 )

x-1 = 0 // + 1

x = 1

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 1} 

x = 3

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