(a+2)/(a^2-3a+9)-(2a+16)/(a^3+27)

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вопрос

To simplify this expression, we'll need to find a common denominator for the two fractions. The first fraction already has the denominator of a^2 - 3a + 9, so we just need to factorize the denominator of the second fraction, a^3 + 27, and express the second fraction with the common denominator of a^2 - 3a + 9.

a^3 + 27 can be factored as (a+3)(a^2 - 3a + 9), so the second fraction can be expressed as:

(2a + 16)/(a^3 + 27) = (2a + 16)/[(a+3)(a^2 - 3a + 9)]

Now, let's combine the fractions using the common denominator of a^2 - 3a + 9:

[(a+2)/(a^2 - 3a + 9)] - [(2a+16)/[(a+3)(a^2 - 3a + 9)]]

= [(a+2)(a+3) - (2a+16)]/(a+3)(a^2 - 3a + 9)

= [a^2 + 3a + 2a + 6 - 2a - 16]/(a+3)(a^2 - 3a + 9)

= [a^2 + a - 10]/(a+3)(a^2 - 3a + 9)

Therefore, the simplified expression is (a^2 + a - 10)/(a+3)(a^2 - 3a + 9).