What is the answer to ((x^2-6))/x-((3x))/((x^2-6))=-2 ?

The answer to ((x^2-6))/x-((3x))/((x^2-6))=-2 is x=-2,x=3,x=(-3+sqrt(33))/2 ,x=(-3-sqrt(33))/2

Solve for x: ((x^2-6))/x-((3x))/((x^2-6))=-2

The solution is x=-2,x=3,x=(-3+sqrt(33))/2 ,x=(-3-sqrt(33))/2

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\frac{( x ^{2} - 6 )}{x} - \frac{( 3 x )}{( x ^{2} - 6 )} = - 2

x = - 2, x = 3, x = \frac{- 3 + 33}{2}, x = \frac{- 3 - 33}{2}

Decimal Notation

x = - 2, x = 3, x = 1.37228 \dots, x = - 4.37228 \dots

Solution steps

\frac{( x ^{2} - 6 )}{x} - \frac{( 3 x )}{( x ^{2} - 6 )} = - 2

Multiply by LCM

(x^{2} - 6) (x + 6) (x - 6) - 3 x^{2} = - 2 x (x + 6) (x - 6)

Solve

(x^{2} - 6) (x + 6) (x - 6) - 3 x^{2} = - 2 x (x + 6) (x - 6) : x = - 2, x = 3, x = \frac{- 3 + 33}{2}, x = \frac{- 3 - 33}{2}

x = - 2, x = 3, x = \frac{- 3 + 33}{2}, x = \frac{- 3 - 33}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 6, x = - 6

Combine undefined points with solutions:

x = - 2, x = 3, x = \frac{- 3 + 33}{2}, x = \frac{- 3 - 33}{2}

\frac{( 3 x + 7 )}{( x + 2 ) + x} = \frac{1}{( x + 2 ) + 8}

\frac{( x + 1 )}{3} = \frac{21}{2 + 2 x - 1}

a, (a + b)^{- 1} = a^{- 1} + b^{- 1}

\frac{4}{x ^{2}} = \frac{1}{( a - x ) 2}

\frac{12}{23} = \frac{0.5}{x}

What is the answer to ((x^2-6))/x-((3x))/((x^2-6))=-2 ?
The answer to ((x^2-6))/x-((3x))/((x^2-6))=-2 is x=-2,x=3,x=(-3+sqrt(33))/2 ,x=(-3-sqrt(33))/2
Solve for x: ((x^2-6))/x-((3x))/((x^2-6))=-2
The solution is x=-2,x=3,x=(-3+sqrt(33))/2 ,x=(-3-sqrt(33))/2