3x/(x-5)+15/(x+5)=-102/(x^2-25)

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Solution for 3x/(x-5)+15/(x+5)=-102/(x^2-25) equation: 


D( x )

x-5 = 0

x+5 = 0

x^2-25 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x^2-25 = 0

x^2-25 = 0

1*x^2 = 25 // : 1

x^2 = 25

x^2 = 25 // ^ 1/2

abs(x) = 5

x = 5 or x = -5

x in (-oo:-5) U (-5:5) U (5:+oo)

(3*x)/(x-5)+15/(x+5) = -102/(x^2-25) // + -102/(x^2-25)

(3*x)/(x-5)+15/(x+5)-(-102/(x^2-25)) = 0

(3*x)/(x-5)+15/(x+5)+102*(x^2-25)^-1 = 0

(3*x)/(x-5)+15/(x+5)+102/(x^2-25) = 0

(3*x*(x+5)*(x^2-25))/((x-5)*(x+5)*(x^2-25))+(15*(x-5)*(x^2-25))/((x-5)*(x+5)*(x^2-25))+(102*(x-5)*(x+5))/((x-5)*(x+5)*(x^2-25)) = 0

3*x*(x+5)*(x^2-25)+15*(x-5)*(x^2-25)+102*(x-5)*(x+5) = 0

3*x^4+30*x^3-150*x^2+102*x^2-750*x-2550+1875 = 0

3*x^4+30*x^3-48*x^2-750*x-675 = 0

3*x^4+30*x^3-48*x^2-750*x-675 = 0

3*(x^4+10*x^3-16*x^2-250*x-225) = 0

x^4+10*x^3-16*x^2-250*x-225 = 0

{ 1, -1, 3, -3, 5, -5, 9, -9, 15, -15, 25, -25, 45, -45, 75, -75, 225, -225 }

1

x = 1

x^4+10*x^3-16*x^2-250*x-225 = -480

1

-1

x = -1

x^4+10*x^3-16*x^2-250*x-225 = 0

-1

x+1

x^3+9*x^2-25*x-225

x^4+10*x^3-16*x^2-250*x-225

x+1

-x^4-x^3

9*x^3-16*x^2-250*x-225

-9*x^3-9*x^2

-25*x^2-250*x-225

25*x^2+25*x

-225*x-225

225*x+225

0

x^3+9*x^2-25*x-225 = 0

{ 1, -1, 3, -3, 5, -5, 9, -9, 15, -15, 25, -25, 45, -45, 75, -75, 225, -225 }

1

x = 1

x^3+9*x^2-25*x-225 = -240

1

-1

x = -1

x^3+9*x^2-25*x-225 = -192

-1

3

x = 3

x^3+9*x^2-25*x-225 = -192

3

-3

x = -3

x^3+9*x^2-25*x-225 = -96

-3

5

x = 5

x^3+9*x^2-25*x-225 = 0

5

x-5

x^2+14*x+45

x^3+9*x^2-25*x-225

x-5

5*x^2-x^3

14*x^2-25*x-225

70*x-14*x^2

45*x-225

225-45*x

0

x^2+14*x+45 = 0

DELTA = 14^2-(1*4*45)

DELTA = 16

DELTA > 0

x = (16^(1/2)-14)/(1*2) or x = (-16^(1/2)-14)/(1*2)

x = -5 or x = -9

x in { -9, -5, -1, 5} 

3*(x+9)*(x+5)*(x+1)*(x-5) = 0

(3*(x+9)*(x+5)*(x+1)*(x-5))/((x-5)*(x+5)*(x^2-25)) = 0

(3*(x+9)*(x+5)*(x+1)*(x-5))/((x-5)*(x+5)*(x^2-25)) = 0 // * (x-5)*(x+5)*(x^2-25)

3*(x+9)*(x+5)*(x+1)*(x-5) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x+5 )

x+5 = 0 // - 5

x = -5

( x+9 )

x+9 = 0 // - 9

x = -9

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -5} 

x in { 5} 

x in { -1, -9 }

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