1/(2x+10)=8/(x^2-25)-2/(x-5)

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Solution for 1/(2x+10)=8/(x^2-25)-2/(x-5) equation: 


D( x )

x-5 = 0

2*x+10 = 0

x^2-25 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

2*x+10 = 0

2*x+10 = 0

2*x+10 = 0 // - 10

2*x = -10 // : 2

x = -10/2

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)

1/(2*x+10) = 8/(x^2-25)-(2/(x-5)) // - 8/(x^2-25)-(2/(x-5))

1/(2*x+10)-(8/(x^2-25))+2/(x-5) = 0

1/(2*x+10)-8*(x^2-25)^-1+2/(x-5) = 0

1/(2*x+10)-8/(x^2-25)+2/(x-5) = 0

(1*(x^2-25)*(x-5))/((2*x+10)*(x^2-25)*(x-5))+(-8*(2*x+10)*(x-5))/((2*x+10)*(x^2-25)*(x-5))+(2*(2*x+10)*(x^2-25))/((2*x+10)*(x^2-25)*(x-5)) = 0

1*(x^2-25)*(x-5)-8*(2*x+10)*(x-5)+2*(2*x+10)*(x^2-25) = 0

x^3+4*x^3-21*x^2+20*x^2-25*x-100*x-500+525 = 0

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

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

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

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

1

x = 1

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

1

-1

x = -1

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

-1

5

x = 5

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

5

x-5

5*x^2+24*x-5

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

x-5

25*x^2-5*x^3

24*x^2-125*x+25

120*x-24*x^2

25-5*x

5*x-25

0

5*x^2+24*x-5 = 0

DELTA = 24^2-(-5*4*5)

DELTA = 676

DELTA > 0

x = (676^(1/2)-24)/(2*5) or x = (-676^(1/2)-24)/(2*5)

x = 1/5 or x = -5

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

(x+5)*(x-1/5)*(x-5) = 0

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

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

(x+5)*(x-1/5)*(x-5) = 0

( x+5 )

x+5 = 0 // - 5

x = -5

( x-1/5 )

x-1/5 = 0 // + 1/5

x = 1/5

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -5} 

x in { 5} 

x = 1/5

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