(4/(x-5))+((3/x+5))=40/(x^2-25)

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Solution for (4/(x-5))+((3/x+5))=40/(x^2-25) equation: 


D( x )

x-5 = 0

x = 0

x^2-25 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x = 0

x = 0

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 (-5:0) U (0:5) U (5:+oo)

4/(x-5)+3/x+5 = 40/(x^2-25) // - 40/(x^2-25)

4/(x-5)-(40/(x^2-25))+3/x+5 = 0

4/(x-5)-40*(x^2-25)^-1+3/x+5 = 0

4/(x-5)-40/(x^2-25)+3/x+5 = 0

(4*x*(x^2-25))/(x*(x-5)*(x^2-25))+(-40*x*(x-5))/(x*(x-5)*(x^2-25))+(3*(x-5)*(x^2-25))/(x*(x-5)*(x^2-25))+(5*x*(x-5)*(x^2-25))/(x*(x-5)*(x^2-25)) = 0

4*x*(x^2-25)-40*x*(x-5)+3*(x-5)*(x^2-25)+5*x*(x-5)*(x^2-25) = 0

5*x^4+4*x^3+3*x^3-25*x^3-40*x^2-15*x^2-125*x^2+100*x-75*x+625*x+375 = 0

5*x^4+7*x^3-25*x^3-55*x^2-125*x^2+25*x+625*x+375 = 0

5*x^4-18*x^3-180*x^2+650*x+375 = 0

5*x^4-18*x^3-180*x^2+650*x+375 = 0

5*x^4-18*x^3-180*x^2+650*x+375 = 0

{ 1, -1, 3, -3, 5, -5, 15, -15, 25, -25, 75, -75, 125, -125, 375, -375 }

1

x = 1

5*x^4-18*x^3-180*x^2+650*x+375 = 832

1

-1

x = -1

5*x^4-18*x^3-180*x^2+650*x+375 = -432

-1

3

x = 3

5*x^4-18*x^3-180*x^2+650*x+375 = 624

3

-3

x = -3

5*x^4-18*x^3-180*x^2+650*x+375 = -2304

-3

5

x = 5

5*x^4-18*x^3-180*x^2+650*x+375 = 0

5

x-5

5*x^3+7*x^2-145*x-75

5*x^4-18*x^3-180*x^2+650*x+375

x-5

25*x^3-5*x^4

7*x^3-180*x^2+650*x+375

35*x^2-7*x^3

650*x-145*x^2+375

145*x^2-725*x

375-75*x

75*x-375

0

5*x^3+7*x^2-145*x-75 = 0

{ 1, -1, 3, -3, 5, -5, 15, -15, 25, -25, 75, -75 }

1

x = 1

5*x^3+7*x^2-145*x-75 = -208

1

-1

x = -1

5*x^3+7*x^2-145*x-75 = 72

-1

3

x = 3

5*x^3+7*x^2-145*x-75 = -312

3

-3

x = -3

5*x^3+7*x^2-145*x-75 = 288

-3

5

x = 5

5*x^3+7*x^2-145*x-75 = 0

5

x-5

5*x^2+32*x+15

5*x^3+7*x^2-145*x-75

x-5

25*x^2-5*x^3

32*x^2-145*x-75

160*x-32*x^2

15*x-75

75-15*x

0

5*x^2+32*x+15 = 0

DELTA = 32^2-(4*5*15)

DELTA = 724

DELTA > 0

x = (724^(1/2)-32)/(2*5) or x = (-724^(1/2)-32)/(2*5)

x = (2*181^(1/2)-32)/10 or x = (-2*181^(1/2)-32)/10

x in { (-2*181^(1/2)-32)/10, (2*181^(1/2)-32)/10, 5, 5} 

(x-((-2*181^(1/2)-32)/10))*(x-((2*181^(1/2)-32)/10))*(x-5)^2 = 0

((x-((-2*181^(1/2)-32)/10))*(x-((2*181^(1/2)-32)/10))*(x-5)^2)/(x*(x-5)*(x^2-25)) = 0

((x-((-2*181^(1/2)-32)/10))*(x-((2*181^(1/2)-32)/10))*(x-5)^2)/(x*(x-5)*(x^2-25)) = 0 // * x*(x-5)*(x^2-25)

(x-((-2*181^(1/2)-32)/10))*(x-((2*181^(1/2)-32)/10))*(x-5)^2 = 0

( x-((-2*181^(1/2)-32)/10) )

x-((-2*181^(1/2)-32)/10) = 0 // + (-2*181^(1/2)-32)/10

x = (-2*181^(1/2)-32)/10

( x-((2*181^(1/2)-32)/10) )

x-((2*181^(1/2)-32)/10) = 0 // + (2*181^(1/2)-32)/10

x = (2*181^(1/2)-32)/10

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 5} 

x in { (-2*181^(1/2)-32)/10, (2*181^(1/2)-32)/10 }

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