(3x+1)/8-10/(x-2)=35/24

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Solution for (3x+1)/8-10/(x-2)=35/24 equation:


D( x )

x-2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x in (-oo:2) U (2:+oo)

(3*x+1)/8-(10/(x-2)) = 35/24 // - 35/24

(3*x+1)/8-(10/(x-2))-(35/24) = 0

(3*x+1)/8-10*(x-2)^-1-35/24 = 0

(3*x+1)/8-10/(x-2)-35/24 = 0

(24*(3*x+1)*(x-2))/(8*24*(x-2))+(-10*8*24)/(8*24*(x-2))+(-35*8*(x-2))/(8*24*(x-2)) = 0

24*(3*x+1)*(x-2)-35*8*(x-2)-10*8*24 = 0

72*x^2-120*x-280*x-1968+560 = 0

72*x^2-400*x-1408 = 0

72*x^2-400*x-1408 = 0

8*(9*x^2-50*x-176) = 0

9*x^2-50*x-176 = 0

DELTA = (-50)^2-(-176*4*9)

DELTA = 8836

DELTA > 0

x = (8836^(1/2)+50)/(2*9) or x = (50-8836^(1/2))/(2*9)

x = 8 or x = -22/9

8*(x+22/9)*(x-8) = 0

(8*(x+22/9)*(x-8))/(8*24*(x-2)) = 0

(8*(x+22/9)*(x-8))/(8*24*(x-2)) = 0 // * 8*24*(x-2)

8*(x+22/9)*(x-8) = 0

( x+22/9 )

x+22/9 = 0 // - 22/9

x = -22/9

( x-8 )

x-8 = 0 // + 8

x = 8

x in { -22/9, 8 }

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