(1/(x-3))+(1/(x-8))=11/24

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Solution for (1/(x-3))+(1/(x-8))=11/24 equation: 


D( x )

x-3 = 0

x-8 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x-8 = 0

x-8 = 0

x-8 = 0 // + 8

x = 8

x in (-oo:3) U (3:8) U (8:+oo)

1/(x-3)+1/(x-8) = 11/24 // - 11/24

1/(x-3)+1/(x-8)-(11/24) = 0

1/(x-3)+1/(x-8)-11/24 = 0

(1*24*(x-8))/(24*(x-3)*(x-8))+(1*24*(x-3))/(24*(x-3)*(x-8))+(-11*(x-3)*(x-8))/(24*(x-3)*(x-8)) = 0

1*24*(x-8)+1*24*(x-3)-11*(x-3)*(x-8) = 0

48*x-11*x^2+121*x-264-264 = 0

169*x-11*x^2-528 = 0

169*x-11*x^2-528 = 0

169*x-11*x^2-528 = 0

DELTA = 169^2-(-528*(-11)*4)

DELTA = 5329

DELTA > 0

x = (5329^(1/2)-169)/(-11*2) or x = (-5329^(1/2)-169)/(-11*2)

x = 48/11 or x = 11

(x-48/11)*(x-11) = 0

((x-48/11)*(x-11))/(24*(x-3)*(x-8)) = 0

((x-48/11)*(x-11))/(24*(x-3)*(x-8)) = 0 // * 24*(x-3)*(x-8)

(x-48/11)*(x-11) = 0

( x-11 )

x-11 = 0 // + 11

x = 11

( x-48/11 )

x-48/11 = 0 // + 48/11

x = 48/11

x in { 11, 48/11 }

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