(x-1)/(x-3)=(12)/(x^2-9)

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Solution for (x-1)/(x-3)=(12)/(x^2-9) equation: 


D( x )

x-3 = 0

x^2-9 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x^2-9 = 0

x^2-9 = 0

1*x^2 = 9 // : 1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

x in (-oo:-3) U (-3:3) U (3:+oo)

(x-1)/(x-3) = 12/(x^2-9) // - 12/(x^2-9)

(x-1)/(x-3)-(12/(x^2-9)) = 0

(x-1)/(x-3)-12*(x^2-9)^-1 = 0

(x-1)/(x-3)-12/(x^2-9) = 0

((x-1)*(x^2-9))/((x-3)*(x^2-9))+(-12*(x-3))/((x-3)*(x^2-9)) = 0

(x-1)*(x^2-9)-12*(x-3) = 0

x^3-x^2-21*x+45 = 0

x^3-x^2-21*x+45 = 0

x^3-x^2-21*x+45 = 0

{ 1, -1, 3, -3, 5, -5, 9, -9, 15, -15, 45, -45 }

1

x = 1

x^3-x^2-21*x+45 = 24

1

-1

x = -1

x^3-x^2-21*x+45 = 64

-1

3

x = 3

x^3-x^2-21*x+45 = 0

3

x-3

x^2+2*x-15

x^3-x^2-21*x+45

x-3

3*x^2-x^3

2*x^2-21*x+45

6*x-2*x^2

45-15*x

15*x-45

0

x^2+2*x-15 = 0

DELTA = 2^2-(-15*1*4)

DELTA = 64

DELTA > 0

x = (64^(1/2)-2)/(1*2) or x = (-64^(1/2)-2)/(1*2)

x = 3 or x = -5

x in { -5, 3, 3} 

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

((x+5)*(x-3)^2)/((x-3)*(x^2-9)) = 0

((x+5)*(x-3)^2)/((x-3)*(x^2-9)) = 0 // * (x-3)*(x^2-9)

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

( x+5 )

x+5 = 0 // - 5

x = -5

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3} 

x = -5

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