# How do you simplify #(x-1)/(x^2-1)+2/(5x+5)#?

Your starting expression is

Focus on the first fraction first. Notice that the denominator is the difference of two squares, since

As you know, the difference of two squares can be factored as

This means that the first fraction is equivalent to

Next, focus on the second fraction. In this case, the denominator can be factored as

The expression can thus be written as

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To simplify the expression (x-1)/(x^2-1)+2/(5x+5), we first factor the denominators. The denominator x^2-1 can be factored as (x-1)(x+1), and the denominator 5x+5 can be factored as 5(x+1).

Next, we find the least common denominator (LCD) of the two fractions, which is (x-1)(x+1)(5x+5).

To make the fractions have a common denominator, we multiply the first fraction by (5x+5)/(5x+5), and the second fraction by (x-1)(x+1)/((x-1)(x+1)).

After simplifying, we get ((x-1)(5x+5)+2(x-1)(x+1))/((x-1)(x+1)(5x+5)).

Expanding and combining like terms in the numerator, we have (5x^2-5+2x^2-2)/(5x^2-5).

Simplifying further, we get (7x^2-7)/(5x^2-5).

This expression cannot be simplified any further.

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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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