# How do you simplify #x/(x-8) - 2/(x+7)#?

Cross multiply to get a common denominator

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To simplify the expression x/(x-8) - 2/(x+7), you need to find a common denominator for the two fractions. The common denominator is (x-8)(x+7).

Next, multiply the numerator and denominator of the first fraction, x/(x-8), by (x+7). This gives you (x(x+7))/((x-8)(x+7)).

Similarly, multiply the numerator and denominator of the second fraction, 2/(x+7), by (x-8). This gives you (2(x-8))/((x-8)(x+7)).

Now, you can combine the two fractions by subtracting the second fraction from the first fraction:

(x(x+7))/((x-8)(x+7)) - (2(x-8))/((x-8)(x+7)).

To simplify further, you can combine the numerators over the common denominator:

(x(x+7) - 2(x-8))/((x-8)(x+7)).

Expanding the numerator gives you:

(x^2 + 7x - 2x + 16)/((x-8)(x+7)).

Combining like terms in the numerator:

(x^2 + 5x + 16)/((x-8)(x+7)).

Therefore, the simplified expression is (x^2 + 5x + 16)/((x-8)(x+7)).

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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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