Equivalent Expression Calculation

How to calculate the equivalent expression?

Given the expression [tex]\dfrac{x^5 - x^3 + 4x^2 - 2}{x^3+3}[/tex], we need to find the equivalent expression.

Calculation Process

To determine the equivalent expression, we can utilize the long division method. Let's break down the steps:

  • Set up the long division with the given expression and divisor.
  • Proceed with the division process by dividing the terms.
  • Write down the results and continue until you reach the final expression.
  • Obtain the equivalent expression from the calculated values.

Detailed Explanation

When we divide [tex]\dfrac{x^5 - x^3 + 4x^2 - 2}{x^3+3}[/tex] using long division, the process involves dividing the terms to simplify the expression.

We follow the steps of long division to get the equivalent expression, which results in [tex]x^2 - 1 + \dfrac{x^2 + 1}{x^3+3}[/tex].

Therefore, the equivalent expression calculation involves a systematic approach to simplify and represent the given expression in a different format for ease of analysis.

By following the long division method and logical reasoning, we arrive at the equivalent expression that accurately reflects the original expression.

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