(1/(x))+(1/(x+1))=(13/42)

Solution for (1/(x))+(1/(x+1))=(13/42) equation:

D( x )

x = 0

x+1 = 0

x = 0

x = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x in (-oo:-1) U (-1:0) U (0:+oo)

1/(x+1)+1/x = 13/42 // - 13/42

1/(x+1)+1/x-(13/42) = 0

1/(x+1)+1/x-13/42 = 0

(1*42*x)/(42*x*(x+1))+(1*42*(x+1))/(42*x*(x+1))+(-13*x*(x+1))/(42*x*(x+1)) = 0

1*42*(x+1)-13*x*(x+1)+1*42*x = 0

84*x-13*x^2-13*x+42 = 0

71*x-13*x^2+42 = 0

71*x-13*x^2+42 = 0

71*x-13*x^2+42 = 0

DELTA = 71^2-(-13*4*42)

DELTA = 7225

DELTA > 0

x = (7225^(1/2)-71)/(-13*2) or x = (-7225^(1/2)-71)/(-13*2)

x = -7/13 or x = 6

(x+7/13)*(x-6) = 0

((x+7/13)*(x-6))/(42*x*(x+1)) = 0

((x+7/13)*(x-6))/(42*x*(x+1)) = 0 // * 42*x*(x+1)

(x+7/13)*(x-6) = 0

( x+7/13 )

x+7/13 = 0 // - 7/13

x = -7/13

( x-6 )

x-6 = 0 // + 6

x = 6

x in { -7/13, 6 }