# How do you simplify #((x/y) - (4/x)) / ((1/x) - (2/y^2))#?

Before you can do the division of the numerator by the denominator, you have to have one fraction at the top and one at the bottom. The calculation can be shown as:

To divide fractions, multiply by the reciprocal of the second fraction:

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To simplify the expression ((x/y) - (4/x)) / ((1/x) - (2/y^2)), we can follow these steps:

- Find a common denominator for each fraction within the expression.
- Simplify each fraction by multiplying the numerator and denominator by the common denominator.
- Combine the fractions by subtracting the numerators over the common denominator.
- Simplify the resulting fraction if possible.

Let's go through the steps:

- The common denominator for the first fraction (x/y) and the second fraction (4/x) is xy.
- Simplifying the first fraction: ((x/y) * (xy)) / (xy) = (x^2) / xy. Simplifying the second fraction: ((4/x) * (xy)) / (xy) = (4y) / xy.
- Combining the fractions: ((x^2) / xy) - ((4y) / xy) = (x^2 - 4y) / xy.
- The resulting simplified expression is (x^2 - 4y) / xy.

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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.

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.

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.

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