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Which expression is equal to 2x/(x+2) − (x−3)/(x+5)?

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Final answer:

To simplify 2x/(x+2) - (x-3)/(x+5), we find a common denominator, rewrite the fractions, and expand the numerators. After simplification, we get (x² + 5x - 6) / ((x+2)(x+5)) which is already in its simplest form as the numerator and denominator have no common factors.

Step-by-step explanation:

We are asked to simplify the expression 2x/(x+2) - (x-3)/(x+5). To do so, we need to find a common denominator which, in this case, will be (x+2)(x+5). We'll then rewrite each fraction with this common denominator and simplify the result.

First, multiply 2x by (x+5)/(x+5) and (x-3) by (x+2)/(x+2) to get equivalent fractions with the common denominator. The expression will then look like this:

((2x)(x+5) - (x-3)(x+2)) / ((x+2)(x+5))

Next, we expand the numerators:

(2x² + 10x - x² - 2x - 3x - 6) / ((x+2)(x+5))

This simplifies to:

(x² + 5x - 6) / ((x+2)(x+5))

We can then factor the numerator if possible and simplify further. However, since x² + 5x - 6 doesn't have factors in common with the denominator, the expression is already in its simplest form.

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