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

Question

how do you solve?

Answer 1

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)]

Answer 2

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)