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

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To simplify the expression (2)/(x) + (2)/(x-1) - (2)/(x-2), we need to find a common denominator for all three fractions. The common denominator is x(x-1)(x-2).

Multiplying the first fraction by (x-1)(x-2)/(x-1)(x-2), the second fraction by x(x-2)/(x(x-2)), and the third fraction by x(x-1)/(x(x-1)), we get:

(2(x-1)(x-2))/(x(x-1)(x-2)) + (2x(x-2))/(x(x-1)(x-2)) - (2x(x-1))/(x(x-1)(x-2))

Combining the numerators, we have:

(2(x-1)(x-2) + 2x(x-2) - 2x(x-1))/(x(x-1)(x-2))

Expanding and simplifying the numerator, we get:

(2x^2 - 4x + 2x^2 - 4x - 2x^2 + 2x)/(x(x-1)(x-2))

Combining like terms, we have:

(-4x)/(x(x-1)(x-2))

Therefore, the simplified expression is (-4x)/(x(x-1)(x-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.

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