((12)/(1-x))+((3x)/(x-1))

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Solution for ((12)/(1-x))+((3x)/(x-1)) equation: 


D( x )

1-x = 0

x-1 = 0

1-x = 0

1-x = 0

1-x = 0 // - 1

-x = -1 // * -1

x = 1

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

12/(1-x)+(3*x)/(x-1) = 0

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

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

15*x-3*x^2-12 = 0

15*x-3*x^2-12 = 0

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

5*x-x^2-4 = 0

DELTA = 5^2-(-4*(-1)*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)-5)/(-1*2) or x = (-9^(1/2)-5)/(-1*2)

x = 1 or x = 4

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

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

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

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

( x-1 )

x-1 = 0 // + 1

x = 1

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 1} 

x = 4

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