(4x/x^2-9)-(6/x^2+x-12)

Solution for (4x/x^2-9)-(6/x^2+x-12) equation:

D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

(4*x)/(x^2)-x-(6/(x^2))-9+12 = 0

(4*x)/(x^2)-x-6*x^-2-9+12 = 0

4*x^-1-1*x^1-6*x^-2+3*x^0 = 0

(3*x^2-1*x^3+4*x^1-6*x^0)/(x^2) = 0 // * x^4

x^2*(3*x^2-1*x^3+4*x^1-6*x^0) = 0

x^2

3*x^2-x^3+4*x-6 = 0

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

1

x = 1

3*x^2-x^3+4*x-6 = 0

1

x-1

2*x-x^2+6

3*x^2-x^3+4*x-6

x-1

x^3-x^2

2*x^2+4*x-6

2*x-2*x^2

6*x-6

6-6*x

0

2*x-x^2+6 = 0

DELTA = 2^2-(-1*4*6)

DELTA = 28

DELTA > 0

x = (28^(1/2)-2)/(-1*2) or x = (-28^(1/2)-2)/(-1*2)

x = (2*7^(1/2)-2)/(-2) or x = (-2*7^(1/2)-2)/(-2)

x in { (2*7^(1/2)-2)/(-2), (-2*7^(1/2)-2)/(-2), 1} 

x in { (2*7^(1/2)-2)/(-2), (-2*7^(1/2)-2)/(-2), 1 }