1/(x+4)-1/(x+16)=1/24

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Solution for 1/(x+4)-1/(x+16)=1/24 equation: 


D( x )

x+4 = 0

x+16 = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x+16 = 0

x+16 = 0

x+16 = 0 // - 16

x = -16

x in (-oo:-16) U (-16:-4) U (-4:+oo)

1/(x+4)-(1/(x+16)) = 1/24 // - 1/24

1/(x+4)-(1/(x+16))-(1/24) = 0

1/(x+4)-(x+16)^-1-1/24 = 0

1/(x+4)-1/(x+16)-1/24 = 0

(1*24*(x+16))/(24*(x+4)*(x+16))+(-1*24*(x+4))/(24*(x+4)*(x+16))+(-1*(x+4)*(x+16))/(24*(x+4)*(x+16)) = 0

1*24*(x+16)-1*24*(x+4)-1*(x+4)*(x+16) = 0

288-x^2-20*x-64 = 0

224-x^2-20*x = 0

224-x^2-20*x = 0

224-x^2-20*x = 0

DELTA = (-20)^2-(-1*4*224)

DELTA = 1296

DELTA > 0

x = (1296^(1/2)+20)/(-1*2) or x = (20-1296^(1/2))/(-1*2)

x = -28 or x = 8

(x+28)*(x-8) = 0

((x+28)*(x-8))/(24*(x+4)*(x+16)) = 0

((x+28)*(x-8))/(24*(x+4)*(x+16)) = 0 // * 24*(x+4)*(x+16)

(x+28)*(x-8) = 0

( x+28 )

x+28 = 0 // - 28

x = -28

( x-8 )

x-8 = 0 // + 8

x = 8

x in { -28, 8 }

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