# How do you simplify #x/(x+3) - (x+3)/x#?

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To simplify the expression x/(x+3) - (x+3)/x, we can find a common denominator and combine the fractions. The common denominator is x(x+3).

Multiplying the first fraction by (x/x) and the second fraction by ((x+3)/(x+3)), we get:

(x^2 - (x+3)^2) / (x(x+3))

Expanding (x+3)^2 gives:

(x^2 - (x^2 + 6x + 9)) / (x(x+3))

Simplifying further:

(x^2 - x^2 - 6x - 9) / (x(x+3))

(-6x - 9) / (x(x+3))

This is the simplified form of the expression x/(x+3) - (x+3)/x.

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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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