# How do you simplify #(a+2)/(a-4) + (a-2)/(a+3)#?

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To simplify the expression (a+2)/(a-4) + (a-2)/(a+3), we need to find a common denominator for the two fractions. The common denominator is (a-4)(a+3).

Next, we can rewrite the fractions with the common denominator:

[(a+2)(a+3)]/[(a-4)(a+3)] + [(a-2)(a-4)]/[(a-4)(a+3)]

Expanding the numerators, we get:

[(a^2 + 5a + 6)]/[(a-4)(a+3)] + [(a^2 - 6a + 8)]/[(a-4)(a+3)]

Combining the fractions, we have:

[(a^2 + 5a + 6) + (a^2 - 6a + 8)]/[(a-4)(a+3)]

Simplifying the numerator, we get:

(2a^2 - a + 14)/[(a-4)(a+3)]

Therefore, the simplified expression is (2a^2 - a + 14)/[(a-4)(a+3)].

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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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