# How do you simplify #n/(2n+10)+1/(n^2-25)#?

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To simplify the expression n/(2n+10) + 1/(n^2-25), we can follow these steps:

Step 1: Factor the denominators. The denominator 2n+10 can be factored as 2(n+5), and the denominator n^2-25 can be factored as (n+5)(n-5).

Step 2: Find the least common denominator (LCD). The LCD is the product of the distinct factors from both denominators, which in this case is 2(n+5)(n-5).

Step 3: Rewrite the fractions with the LCD as the denominator. n/(2n+10) can be rewritten as n/2(n+5), and 1/(n^2-25) can be rewritten as 1/(n+5)(n-5).

Step 4: Multiply each fraction by the appropriate factor to eliminate the denominators. For n/2(n+5), we multiply the numerator and denominator by 2(n-5), and for 1/(n+5)(n-5), we multiply the numerator and denominator by 2.

Step 5: Simplify the resulting expression. After performing the multiplication, the expression becomes (n(n-5) + 2) / 2(n+5)(n-5).

Therefore, the simplified expression is (n^2 - 5n + 2) / 2(n+5)(n-5).

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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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