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How do you solve #-x / 2 + 1 / (2x) = -4 / x#?

Answer 1

#x = +-3#

When dealing with equations that contain fractions, we can eliminate the fractions right away by multiplying each term by the denominator's lowest common multiple, which allows us to cancel out each denominator.

In this case the LCM is #2x#

#(-x xx color(red)(2x))/2 +(1xx color(red)(2x))/(2x) = -(4xx color(red)(2x))/x#

#(-x xx color(red)(cancel2x))/cancel2 +(1xx color(red)(cancel(2x)))/(cancel(2x)) = -(4xx color(red)(2cancelx))/cancelx#

#-x^2 +1 =-8#

#-x^2 = -9 rArr x^2 = 9 " or " x^2 -9 = 0#

#x = +-sqrt 9 " "(x+3)(x-3) = 0#

#x = +-3#

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Answer 2

Julia Adams

To solve the equation -x / 2 + 1 / (2x) = -4 / x, we can start by multiplying every term in the equation by the least common denominator, which is 2x. This will help us eliminate the denominators.

By doing so, we get -x * (2x) / 2 + (1 / (2x)) * (2x) = (-4 / x) * (2x).

Simplifying this equation gives us -x^2 + 1 = -8.

Rearranging the equation, we have -x^2 = -9.

To solve for x, we can multiply both sides of the equation by -1, which gives us x^2 = 9.

Taking the square root of both sides, we find x = ±3.

Therefore, the solutions to the equation are x = 3 and x = -3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.