4x/(x-5)-20/(x+5)=200/(x^2-25)

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Solution for 4x/(x-5)-20/(x+5)=200/(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)

(4*x)/(x-5)-(20/(x+5)) = 200/(x^2-25) // - 200/(x^2-25)

(4*x)/(x-5)-(20/(x+5))-(200/(x^2-25)) = 0

(4*x)/(x-5)-20*(x+5)^-1-200*(x^2-25)^-1 = 0

(4*x)/(x-5)-20/(x+5)-200/(x^2-25) = 0

(4*x*(x+5)*(x^2-25))/((x-5)*(x+5)*(x^2-25))+(-20*(x-5)*(x^2-25))/((x-5)*(x+5)*(x^2-25))+(-200*(x-5)*(x+5))/((x-5)*(x+5)*(x^2-25)) = 0

4*x*(x+5)*(x^2-25)-20*(x-5)*(x^2-25)-200*(x-5)*(x+5) = 0

4*x^4-200*x^2-2500+5000 = 0

4*x^4-200*x^2+2500 = 0

4*x^4-200*x^2+2500 = 0

4*(x^4-50*x^2+625) = 0

x^4-50*x^2+625 = 0

{ 1, -1, 5, -5, 25, -25, 125, -125, 625, -625 }

1

x = 1

x^4-50*x^2+625 = 576

1

-1

x = -1

x^4-50*x^2+625 = 576

-1

5

x = 5

x^4-50*x^2+625 = 0

5

x-5

x^3+5*x^2-25*x-125

x^4-50*x^2+625

x-5

5*x^3-x^4

5*x^3-50*x^2+625

25*x^2-5*x^3

625-25*x^2

25*x^2-125*x

625-125*x

125*x-625

0

x^3+5*x^2-25*x-125 = 0

{ 1, -1, 5, -5, 25, -25, 125, -125 }

1

x = 1

x^3+5*x^2-25*x-125 = -144

1

-1

x = -1

x^3+5*x^2-25*x-125 = -96

-1

5

x = 5

x^3+5*x^2-25*x-125 = 0

5

x-5

x^2+10*x+25

x^3+5*x^2-25*x-125

x-5

5*x^2-x^3

10*x^2-25*x-125

50*x-10*x^2

25*x-125

125-25*x

0

x^2+10*x+25 = 0

DELTA = 10^2-(1*4*25)

DELTA = 0

x = -10/(1*2)

x = -5 or x = -5

x in { -5, -5, 5, 5} 

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

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

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

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

( x+5 )

x+5 = 0 // - 5

x = -5

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -5} 

x in { 5} 

x belongs to the empty set

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