(6/x)+(8/(x+5))=3

Solution for (6/x)+(8/(x+5))=3 equation:

D( x )

x+5 = 0

x = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x = 0

x = 0

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

8/(x+5)+6/x = 3 // - 3

8/(x+5)+6/x-3 = 0

(8*x)/(x*(x+5))+(6*(x+5))/(x*(x+5))+(-3*x*(x+5))/(x*(x+5)) = 0

6*(x+5)-3*x*(x+5)+8*x = 0

14*x-3*x^2-15*x+30 = 0

30-3*x^2-x = 0

30-3*x^2-x = 0

30-3*x^2-x = 0

DELTA = (-1)^2-(-3*4*30)

DELTA = 361

DELTA > 0

x = (361^(1/2)+1)/(-3*2) or x = (1-361^(1/2))/(-3*2)

x = -10/3 or x = 3

(x+10/3)*(x-3) = 0

((x+10/3)*(x-3))/(x*(x+5)) = 0

((x+10/3)*(x-3))/(x*(x+5)) = 0 // * x*(x+5)

(x+10/3)*(x-3) = 0

( x+10/3 )

x+10/3 = 0 // - 10/3

x = -10/3

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -10/3, 3 }