(1)/(x-3)+(1)/(x+5)=(3)/(5)

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Solution for (1)/(x-3)+(1)/(x+5)=(3)/(5) equation: 


D( x )

x+5 = 0

x-3 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x in (-oo:-5) U (-5:3) U (3:+oo)

1/(x-3)+1/(x+5) = 3/5 // - 3/5

1/(x-3)+1/(x+5)-(3/5) = 0

1/(x-3)+1/(x+5)-3/5 = 0

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

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

10*x-3*x^2-6*x+10+45 = 0

4*x-3*x^2+55 = 0

4*x-3*x^2+55 = 0

4*x-3*x^2+55 = 0

DELTA = 4^2-(-3*4*55)

DELTA = 676

DELTA > 0

x = (676^(1/2)-4)/(-3*2) or x = (-676^(1/2)-4)/(-3*2)

x = -11/3 or x = 5

(x+11/3)*(x-5) = 0

((x+11/3)*(x-5))/(5*(x-3)*(x+5)) = 0

((x+11/3)*(x-5))/(5*(x-3)*(x+5)) = 0 // * 5*(x-3)*(x+5)

(x+11/3)*(x-5) = 0

( x+11/3 )

x+11/3 = 0 // - 11/3

x = -11/3

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -11/3, 5 }

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