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

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Solution for 4/(x^2-10x+25)-1/(x^2-25)=1/(x+5) equation: 


D( x )

x+5 = 0

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

x^2-25 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

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

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

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

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

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

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

x^2-10*x+25 = 0

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

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

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

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

3*x^3-x^4+10*x^3+25*x^2-75*x-250*x-625+625 = 0

13*x^3-x^4+25*x^2-325*x = 0

13*x^3-x^4+25*x^2-325*x = 0

x*(13*x^2-x^3+25*x-325) = 0

13*x^2-x^3+25*x-325 = 0

{ 1, -1, 5, -5, 13, -13, 25, -25, 65, -65, 325, -325 }

1

x = 1

13*x^2-x^3+25*x-325 = -288

1

-1

x = -1

13*x^2-x^3+25*x-325 = -336

-1

5

x = 5

13*x^2-x^3+25*x-325 = 0

5

x-5

8*x-x^2+65

13*x^2-x^3+25*x-325

x-5

x^3-5*x^2

8*x^2+25*x-325

40*x-8*x^2

65*x-325

325-65*x

0

8*x-x^2+65 = 0

DELTA = 8^2-(-1*4*65)

DELTA = 324

DELTA > 0

x = (324^(1/2)-8)/(-1*2) or x = (-324^(1/2)-8)/(-1*2)

x = -5 or x = 13

x in { -5, 13, 5} 

x*(x+5)*(x-13)*(x-5) = 0

(x*(x+5)*(x-13)*(x-5))/((x-5)^2*(x^2-25)*(x+5)) = 0

(x*(x+5)*(x-13)*(x-5))/((x-5)^2*(x^2-25)*(x+5)) = 0 // * (x-5)^2*(x^2-25)*(x+5)

x*(x+5)*(x-13)*(x-5) = 0

( x+5 )

x+5 = 0 // - 5

x = -5

( x-13 )

x-13 = 0 // + 13

x = 13

( x-5 )

x-5 = 0 // + 5

x = 5

( x )

x = 0

x in { -5} 

x in { 5} 

x in { 13, 0 }

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