Question

A+3/a^2+3a+9 - 1/a-3 + a^3+3a-9/a^3-27=​

Answer 1

Ответ:

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Объяснение:

Answer 2

To simplify the expression, we need to find a common denominator and then combine the fractions. The denominators in this expression are a^2 + 3a + 9, a - 3, and a^3 - 27. First, let's factor the denominators to make the simplification easier:

1. a^2 + 3a + 9 can't be factored further.

2. a - 3 is already in its simplest form.

3. a^3 - 27 is the difference of cubes, which can be factored as (a - 3)(a^2 + 3a + 9).

Now, let's rewrite the fractions with common denominators:

A + 3/(a^2 + 3a + 9) - 1/(a - 3) + (a^3 + 3a - 9)/(a - 3)(a^2 + 3a + 9)

Now that all fractions have a common denominator, we can combine them into a single fraction:

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

Now, let's simplify the numerator:

[A(a - 3) + 3 - (a^3 + 3a - 9)] = A(a - 3) + 3 - a^3 - 3a + 9

Now, combine like terms:

A(a - 3 - 3a) + 3 + 9 - a^3

Simplify further:

A(-2a - 3) + 12 - a^3

Now, distribute the A:

-2aA - 3A + 12 - a^3

So, the simplified expression is:

(-2aA - 3A + 12 - a^3) / [(a - 3)(a^2 + 3a + 9)]