(5x/(x^2-9))=(15/(x^2-9))-(4/x+3)

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Solution for (5x/(x^2-9))=(15/(x^2-9))-(4/x+3) equation: 


D( x )

x = 0

x^2-9 = 0

x = 0

x = 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 in (-oo:-3) U (-3:0) U (0:3) U (3:+oo)

(5*x)/(x^2-9) = 15/(x^2-9)-(4/x)-3 // - 15/(x^2-9)-(4/x)-3

(5*x)/(x^2-9)-(15/(x^2-9))+4/x+3 = 0

(5*x)/(x^2-9)-15*(x^2-9)^-1+4/x+3 = 0

(5*x)/(x^2-9)-15/(x^2-9)+4/x+3 = 0

(5*x*x)/(x*(x^2-9))+(-15*x)/(x*(x^2-9))+(4*(x^2-9))/(x*(x^2-9))+(3*x*(x^2-9))/(x*(x^2-9)) = 0

4*(x^2-9)+3*x*(x^2-9)+5*x*x-15*x = 0

3*x^3+5*x^2+4*x^2-15*x-27*x-36 = 0

3*x^3+9*x^2-15*x-27*x-36 = 0

3*x^3+9*x^2-42*x-36 = 0

3*x^3+9*x^2-42*x-36 = 0

3*(x^3+3*x^2-14*x-12) = 0

x^3+3*x^2-14*x-12 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }

1

x = 1

x^3+3*x^2-14*x-12 = -22

1

-1

x = -1

x^3+3*x^2-14*x-12 = 4

-1

2

x = 2

x^3+3*x^2-14*x-12 = -20

2

-2

x = -2

x^3+3*x^2-14*x-12 = 20

-2

3

x = 3

x^3+3*x^2-14*x-12 = 0

3

x-3

x^2+6*x+4

x^3+3*x^2-14*x-12

x-3

3*x^2-x^3

6*x^2-14*x-12

18*x-6*x^2

4*x-12

12-4*x

0

x^2+6*x+4 = 0

DELTA = 6^2-(1*4*4)

DELTA = 20

DELTA > 0

x = (20^(1/2)-6)/(1*2) or x = (-20^(1/2)-6)/(1*2)

x = (2*5^(1/2)-6)/2 or x = (-2*5^(1/2)-6)/2

x in { (-2*5^(1/2)-6)/2, (2*5^(1/2)-6)/2, 3} 

3*(x-((-2*5^(1/2)-6)/2))*(x-((2*5^(1/2)-6)/2))*(x-3) = 0

(3*(x-((-2*5^(1/2)-6)/2))*(x-((2*5^(1/2)-6)/2))*(x-3))/(x*(x^2-9)) = 0

(3*(x-((-2*5^(1/2)-6)/2))*(x-((2*5^(1/2)-6)/2))*(x-3))/(x*(x^2-9)) = 0 // * x*(x^2-9)

3*(x-((-2*5^(1/2)-6)/2))*(x-((2*5^(1/2)-6)/2))*(x-3) = 0

( x-((-2*5^(1/2)-6)/2) )

x-((-2*5^(1/2)-6)/2) = 0 // + (-2*5^(1/2)-6)/2

x = (-2*5^(1/2)-6)/2

( x-((2*5^(1/2)-6)/2) )

x-((2*5^(1/2)-6)/2) = 0 // + (2*5^(1/2)-6)/2

x = (2*5^(1/2)-6)/2

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3} 

x in { (-2*5^(1/2)-6)/2, (2*5^(1/2)-6)/2 }

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