x/(2x+24)-144/(x^2-144)

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Solution for x/(2x+24)-144/(x^2-144) equation: 


D( x )

2*x+24 = 0

x^2-144 = 0

2*x+24 = 0

2*x+24 = 0

2*x+24 = 0 // - 24

2*x = -24 // : 2

x = -24/2

x = -12

x^2-144 = 0

x^2-144 = 0

1*x^2 = 144 // : 1

x^2 = 144

x^2 = 144 // ^ 1/2

abs(x) = 12

x = 12 or x = -12

x in (-oo:-12) U (-12:12) U (12:+oo)

x/(2*x+24)-(144/(x^2-144)) = 0

x/(2*x+24)-144*(x^2-144)^-1 = 0

x/(2*x+24)-144/(x^2-144) = 0

(x*(x^2-144))/((2*x+24)*(x^2-144))+(-144*(2*x+24))/((2*x+24)*(x^2-144)) = 0

x*(x^2-144)-144*(2*x+24) = 0

x^3-432*x-3456 = 0

x^3-432*x-3456 = 0

x^3-432*x-3456 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 12, -12, 16, -16, 18, -18, 24, -24, 27, -27, 32, -32, 36, -36, 48, -48, 54, -54, 64, -64, 72, -72, 96, -96, 108, -108, 128, -128, 144, -144, 192, -192, 216, -216, 288, -288, 384, -384, 432, -432, 576, -576, 864, -864, 1152, -1152, 1728, -1728, 3456, -3456 }

1

x = 1

x^3-432*x-3456 = -3887

1

-1

x = -1

x^3-432*x-3456 = -3025

-1

2

x = 2

x^3-432*x-3456 = -4312

2

-2

x = -2

x^3-432*x-3456 = -2600

-2

3

x = 3

x^3-432*x-3456 = -4725

3

-3

x = -3

x^3-432*x-3456 = -2187

-3

4

x = 4

x^3-432*x-3456 = -5120

4

-4

x = -4

x^3-432*x-3456 = -1792

-4

6

x = 6

x^3-432*x-3456 = -5832

6

-6

x = -6

x^3-432*x-3456 = -1080

-6

8

x = 8

x^3-432*x-3456 = -6400

8

-8

x = -8

x^3-432*x-3456 = -512

-8

9

x = 9

x^3-432*x-3456 = -6615

9

-9

x = -9

x^3-432*x-3456 = -297

-9

12

x = 12

x^3-432*x-3456 = -6912

12

-12

x = -12

x^3-432*x-3456 = 0

-12

x+12

x^2-12*x-288

x^3-432*x-3456

x+12

-x^3-12*x^2

-12*x^2-432*x-3456

12*x^2+144*x

-288*x-3456

288*x+3456

0

x^2-12*x-288 = 0

DELTA = (-12)^2-(-288*1*4)

DELTA = 1296

DELTA > 0

x = (1296^(1/2)+12)/(1*2) or x = (12-1296^(1/2))/(1*2)

x = 24 or x = -12

x in { -12, 24, -12} 

(x+12)^2*(x-24) = 0

((x+12)^2*(x-24))/((2*x+24)*(x^2-144)) = 0

((x+12)^2*(x-24))/((2*x+24)*(x^2-144)) = 0 // * (2*x+24)*(x^2-144)

(x+12)^2*(x-24) = 0

( x+12 )

x+12 = 0 // - 12

x = -12

( x-24 )

x-24 = 0 // + 24

x = 24

x in { -12} 

x = 24

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