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Escoja la respuesta correcta.

\[
\frac{15x^8 + 10x^5 - 20x^6 + 35x^2}{5x^3} =
\]

A. [tex]3x^3[/tex]
B. [tex]-4x[/tex]
C. [tex]5x[/tex]
D. [tex]\frac{7}{x}[/tex]
E. [tex]-4x^3[/tex]
F. [tex]7x[/tex]
G. [tex]4x[/tex]
H. [tex]2x^2[/tex]

Answer :

To solve the given expression and choose the correct answer, let's break it down step by step.

We have the expression:
[tex]\frac{15x^8 + 10x^5 - 20x^6 + 35x^2}{5x^3}[/tex]

Our task is to simplify the fraction by dividing each term in the numerator by the denominator, [tex]5x^3[/tex].

  1. Divide each term individually by the denominator:

    • [tex]\frac{15x^8}{5x^3} = 3x^{8-3} = 3x^5[/tex]
    • [tex]\frac{10x^5}{5x^3} = 2x^{5-3} = 2x^2[/tex]
    • [tex]\frac{-20x^6}{5x^3} = -4x^{6-3} = -4x^3[/tex]
    • [tex]\frac{35x^2}{5x^3} = 7x^{2-3} = 7x^{-1} = \frac{7}{x}[/tex]

  2. Combine all simplified terms:

    • The simplified expression is:
      [tex]3x^5 + 2x^2 - 4x^3 + \frac{7}{x}[/tex]

Among the provided multiple-choice options, only option [tex]D[/tex], which is [tex]\frac{7}{x}[/tex], matches one of the terms from our simplified expression.

Hence, the correct choice is D. Note that this answer represents only one part of the complete simplified form, but since it corresponds perfectly to the option given and none of the other choices match the entire simplified result, we select it as the answer for this question.

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