# How do you combine #(x-10)/(x-8)-(x+10)/(8-x)#?

See the entire solution process below:

Now that there is a common denominator for each fraction we can subtract the numerators:

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To combine the expressions (x-10)/(x-8) and (x+10)/(8-x), we need to find a common denominator. In this case, the common denominator is (x-8)(8-x).

Next, we can rewrite the fractions with the common denominator:

(x-10)/(x-8) = (x-10)(-1)/((x-8)(-1)) = (-x+10)/(8-x)

(x+10)/(8-x) = -(x+10)/(x-8)

Now, we can combine the fractions by subtracting them:

(-x+10)/(8-x) - (-(x+10)/(x-8))

To subtract the fractions, we need to find a common denominator again, which is (x-8)(8-x).

(-x+10)/(8-x) - (-(x+10)/(x-8)) = ((-x+10)(x-8) - (-(x+10)(8-x)))/((x-8)(8-x))

Simplifying the numerator:

((-x+10)(x-8) - (-(x+10)(8-x))) = (-x^2 + 8x + 10x - 80 + x^2 + 10x - 8x + 80)/((x-8)(8-x))

Combining like terms:

(-x^2 + x^2 + 8x - 8x + 10x + 10x - 80 + 80)/((x-8)(8-x))

Simplifying further:

(20x)/((x-8)(8-x))

Therefore, the combined expression is (20x)/((x-8)(8-x)).

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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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