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

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


D( x )

x^2-9 = 0

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

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

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

x^2-2*x-3 = 0

x^2-2*x-3 = 0

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

DELTA = 16

DELTA > 0

x = (16^(1/2)+2)/(1*2) or x = (2-16^(1/2))/(1*2)

x = 3 or x = -1

x in (-oo:-3) U (-3:-1) U (-1:3) U (3:+oo)

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

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

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

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

x^2-2*x-3 = 0

x^2-2*x-3 = 0

x^2-2*x-3 = 0

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

DELTA = 16

DELTA > 0

x = (16^(1/2)+2)/(1*2) or x = (2-16^(1/2))/(1*2)

x = 3 or x = -1

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

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

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

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

x^3+x^2-15*x+9 = 0

x^3+x^2-15*x+9 = 0

x^3+x^2-15*x+9 = 0

{ 1, -1, 3, -3, 9, -9 }

1

x = 1

x^3+x^2-15*x+9 = -4

1

-1

x = -1

x^3+x^2-15*x+9 = 24

-1

3

x = 3

x^3+x^2-15*x+9 = 0

3

x-3

x^2+4*x-3

x^3+x^2-15*x+9

x-3

3*x^2-x^3

4*x^2-15*x+9

12*x-4*x^2

9-3*x

3*x-9

0

x^2+4*x-3 = 0

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

DELTA = 28

DELTA > 0

x = (28^(1/2)-4)/(1*2) or x = (-28^(1/2)-4)/(1*2)

x = (2*7^(1/2)-4)/2 or x = (-2*7^(1/2)-4)/2

x in { (-2*7^(1/2)-4)/2, (2*7^(1/2)-4)/2, 3} 

(x-((-2*7^(1/2)-4)/2))*(x-((2*7^(1/2)-4)/2))*(x-3) = 0

((x-((-2*7^(1/2)-4)/2))*(x-((2*7^(1/2)-4)/2))*(x-3))/((x+1)*(x-3)*(x^2-9)) = 0

((x-((-2*7^(1/2)-4)/2))*(x-((2*7^(1/2)-4)/2))*(x-3))/((x+1)*(x-3)*(x^2-9)) = 0 // * (x+1)*(x-3)*(x^2-9)

(x-((-2*7^(1/2)-4)/2))*(x-((2*7^(1/2)-4)/2))*(x-3) = 0

( x-((-2*7^(1/2)-4)/2) )

x-((-2*7^(1/2)-4)/2) = 0 // + (-2*7^(1/2)-4)/2

x = (-2*7^(1/2)-4)/2

( x-((2*7^(1/2)-4)/2) )

x-((2*7^(1/2)-4)/2) = 0 // + (2*7^(1/2)-4)/2

x = (2*7^(1/2)-4)/2

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3} 

x in { (-2*7^(1/2)-4)/2, (2*7^(1/2)-4)/2 }

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