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what are the solutions to 1/x^2-4=6/x

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2 Answers

Assume the student meant 1/(x2-4) = 6/x

Cross multiplication leads to x = 6x2 - 24

Collect all terms in one side,

6x2 - x - 24 = 0

Apply quadratic formula,

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

You can either start by multiplying both sides of the equation by x2, or rearrange it this way (both get the same result):

1/x2 - 4 = 6/x               ====>     1/x2 = 6/x + 4 and now multiply both sides by x2

x2*1/x2 = 6x2/x + 4x2    =====>   1 = 6x + 4x2   =====>   0 = 4x2 + 6x -1

Now it's in the form ax2 + bx + c you can use the quadratic formula to find x:

x = [-b ± √(b2 - 4ac)]/(2a)

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