how do you solve?

Assume the student meant 1/(x^{2}-4) = 6/x

Cross multiplication leads to x = 6x^{2} - 24

Collect all terms in one side,

6x^{2} - x - 24 = 0

Apply quadratic formula,

x = (1/12)[1 +/- sqrt(577)]

how do you solve?

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Assume the student meant 1/(x^{2}-4) = 6/x

Cross multiplication leads to x = 6x^{2} - 24

Collect all terms in one side,

6x^{2} - x - 24 = 0

Apply quadratic formula,

x = (1/12)[1 +/- sqrt(577)]

You can either start by multiplying both sides of the equation by x^{2}, or rearrange it this way (both get the same result):

1/x^{2} - 4 = 6/x ====> 1/x^{2} = 6/x + 4 and now multiply both sides by x^{2}

x^{2}*1/x^{2} = 6x^{2}/x + 4x^{2 } =====> 1 = 6x + 4x^{2
}=====> 0 = 4x^{2} + 6x -1

Now it's in the form ax^{2} + bx + c you can use the quadratic formula to find x:

x = [-b ± √(b^{2} - 4ac)]/(2a)