Question

N+3/2n+2 - n + 1/2n - 2 + 3/n^2 - 1; 2a^2+7a+9/a^3-1 + 4a+3/a^2+a+1

Answer 1

Ответ:

Ааааааа у кого-то есть ответ?

Answer 2

To simplify the given expressions, let's handle them one by one:

1. Simplify (N + 3) / (2N + 2) - (N + 1) / (2N - 2) + 3 / (N^2 - 1):

Step 1: Factor the denominators of each fraction if possible.

• (N + 3) / (2N + 2) can be simplified to (N + 3) / 2(N + 1).
• (N + 1) / (2N - 2) can be simplified to (N + 1) / 2(N - 1).
• 3 / (N^2 - 1) can be simplified to 3 / (N + 1)(N - 1) (using difference of squares).

Step 2: Find the common denominator for the fractions. The common denominator is 2(N + 1)(N - 1).

Step 3: Adjust the numerators to have the common denominator.

• (N + 3) / 2(N + 1) can be rewritten as (N + 3)(N - 1) / 2(N + 1)(N - 1).
• (N + 1) / 2(N - 1) can be rewritten as (N + 1)(N + 1) / 2(N + 1)(N - 1).
• 3 / (N + 1)(N - 1) remains the same.

Step 4: Combine the fractions and simplify further. Now we have: [(N + 3)(N - 1) - (N + 1)(N + 1) + 3] / [2(N + 1)(N - 1)].

Expanding the terms: [N^2 - N + 3N - 3 - (N^2 + 2N + 1) + 3] / [2(N + 1)(N - 1)].

Combining like terms: (N^2 - N + 3N - 3 - N^2 - 2N - 1 + 3) / [2(N + 1)(N - 1)].

Simplifying further: (-N) / [2(N + 1)(N - 1)].

The final simplified expression is: -N / [2(N + 1)(N - 1)].

2. Simplify (2a^2 + 7a + 9) / (a^3 - 1) + (4a + 3) / (a^2 + a + 1):

Step 1: Factor the denominators of each fraction if possible.

• a^3 - 1 can be factored as (a - 1)(a^2 + a + 1).

Step 2: Find the common denominator for the fractions. The common denominator is (a - 1)(a^2 + a + 1).

Step 3: Adjust the numerators to have the common denominator.

• (2a^2 + 7a + 9) / (a - 1)(a^2 + a + 1) remains the same.
• (4a + 3) / (a^2 + a + 1) can be rewritten as (4a + 3)(a - 1) / (a - 1)(a^2 + a + 1).

Step 4: Combine the fractions and simplify further. Now we have: (2a^2 + 7a + 9 + (4a + 3)(a - 1)) / [(a - 1)(a^2 + a + 1)].

Expanding the term: (2a^2 + 7a + 9 + 4a^2 + 4a - 4) / [(a - 1)(a^2 + a + 1)].

Combining like terms: (2a^2 + 4a^2 + 7a + 4a + 9 - 4) / [(a - 1)(a^2 + a + 1)].

Simplifying further: (6a^2 + 11a + 5) / [(a - 1)(a^2 + a + 1)].

The final simplified expression is: (6a^2 + 11a + 5) / [(a - 1)(a^2 + a + 1)].