Question

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Answer 1

The sum of the two rational equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).

How to simplify the addition between two rational equations

In this question we must use algebra definitions and theorems to simplify the addition of two rational equations into a single rational equation. Now we proceed to show the procedure of solution in detail:

1. (n + 5) / (n² + 3 · n - 10) + 5 / (3 · n²)      Given
2. (n + 5) / [(n + 5) · (n - 2)] + 5 / (3 · n²)     x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)
3. 1 / (n - 2) + 5 / (3 · n²)     Associative and modulative property / Existence of the multiplicative inverse
4. [3 · n² + 5 · (n - 2)] / [3 · n² · (n - 2)]       Addition of fractions with different denominator
5. (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²)       Distributive property / Power properties / Result

To learn more on rational equations: brainly.com/question/20850120

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