How do you simplify the expression #(b/(b+3)+2)/(b^2-2b-8)#?
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To simplify the expression (b/(b+3)+2)/(b^2-2b-8), you can follow these steps:
- Factor the denominator (b^2-2b-8) as (b-4)(b+2).
- Rewrite the expression as b/(b+3) + 2/(b-4)(b+2).
- Find a common denominator for the fractions, which is (b+3)(b-4)(b+2).
- Multiply the first fraction by (b-4)/(b-4) and the second fraction by (b+3)/(b+3) to get (b(b-4))/((b+3)(b-4)(b+2)) + (2(b+3))/((b+3)(b-4)(b+2)).
- Combine the fractions by adding the numerators: (b(b-4) + 2(b+3))/((b+3)(b-4)(b+2)).
- Simplify the numerator: (b^2 - 4b + 2b + 6)/((b+3)(b-4)(b+2)).
- Combine like terms in the numerator: (b^2 - 2b + 6)/((b+3)(b-4)(b+2)).
- The simplified expression is (b^2 - 2b + 6)/((b+3)(b-4)(b+2)).
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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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