# How do you simplify #2/(x-2) - 3/(x-1)#?

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To simplify the expression 2/(x-2) - 3/(x-1), you need to find a common denominator for the two fractions. The common denominator in this case is (x-2)(x-1).

To get the first fraction with the common denominator, multiply the numerator and denominator by (x-1). This gives you 2(x-1)/[(x-2)(x-1)].

To get the second fraction with the common denominator, multiply the numerator and denominator by (x-2). This gives you 3(x-2)/[(x-2)(x-1)].

Now that both fractions have the same denominator, you can combine them by subtracting the numerators. This gives you [2(x-1) - 3(x-2)]/[(x-2)(x-1)].

Simplifying the numerator further, you get [2x - 2 - 3x + 6]/[(x-2)(x-1)].

Combining like terms in the numerator, you have (-x + 4)/[(x-2)(x-1)].

Therefore, the simplified expression is (-x + 4)/[(x-2)(x-1)].

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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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