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.
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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