2x/x+3+5/x-4=18/x^2+3x

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Solution for 2x/x+3+5/x-4=18/x^2+3x equation:


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

5/x+(2*x)/x-4+3 = 3*x+18/(x^2) // - 3*x+18/(x^2)

5/x-(3*x)-(18/(x^2))+(2*x)/x-4+3 = 0

5/x-3*x-18*x^-2+(2*x)/x-4+3 = 0

5*x^-1-3*x^1-18*x^-2+1*x^0 = 0

(1*x^2-3*x^3+5*x^1-18*x^0)/(x^2) = 0 // * x^4

x^2*(1*x^2-3*x^3+5*x^1-18*x^0) = 0

x^2

x^2-3*x^3+5*x-18 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18 }

1

x = 1

x^2-3*x^3+5*x-18 = -15

1

-1

x = -1

x^2-3*x^3+5*x-18 = -19

-1

2

x = 2

x^2-3*x^3+5*x-18 = -28

2

-2

x = -2

x^2-3*x^3+5*x-18 = 0

-2

x+2

7*x-3*x^2-9

x^2-3*x^3+5*x-18

x+2

3*x^3+6*x^2

7*x^2+5*x-18

-7*x^2-14*x

-9*x-18

9*x+18

0

7*x-3*x^2-9 = 0

DELTA = 7^2-(-9*(-3)*4)

DELTA = -59

DELTA < 0

x in { -2}

x = -2

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