How do you combine #(3n + 8)/(n^2 + 6n + 8) - ( 4n + 2)/(n^2 + n - 12)#?
First factor the denominators.
Multiply each quotient by the appropriate factor to display the common denominator
Expand the numerators using the distributive property (or FOIL if you like).
We can combine the quotients because they have a common denominator.
Combine like terms.
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To combine the given expressions, we need to find a common denominator for both fractions. The denominators are (n^2 + 6n + 8) and (n^2 + n - 12).
The common denominator is (n^2 + 6n + 8)(n^2 + n - 12).
To combine the fractions, we multiply the numerator and denominator of the first fraction by (n^2 + n - 12), and the numerator and denominator of the second fraction by (n^2 + 6n + 8).
This gives us ((3n + 8)(n^2 + n - 12))/((n^2 + 6n + 8)(n^2 + n - 12)) - ((4n + 2)(n^2 + 6n + 8))/((n^2 + 6n + 8)(n^2 + n - 12)).
Next, we simplify the numerators by distributing and combining like terms.
The simplified expression is (3n^3 + 3n^2 - 36n + 8n^2 + 8n - 96 - 4n^3 - 24n^2 - 32n - 8)/(n^4 + 7n^3 - 4n^2 - 96n + 96).
Combining like terms in the numerator gives us (-n^3 - 13n^2 - 60n - 104)/(n^4 + 7n^3 - 4n^2 - 96n + 96).
Therefore, the combined expression is (-n^3 - 13n^2 - 60n - 104)/(n^4 + 7n^3 - 4n^2 - 96n + 96).
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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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