Rational Expressions Answers: Check Your Work

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SUMMARY

The forum discussion centers on the verification of solutions to rational expressions. Key examples include the simplification of \(\frac{5x^2 - 20}{x^2 + 14x + 24}\) to \(\frac{5(x^2 - 4)}{(x + 12)(x + 2)}\), and the multiplication of \(\frac{25}{12x^2y}\) and \(\frac{3y^3}{10x}\) resulting in \(\frac{5y^2}{8x^2}\). Participants emphasize the importance of accurately counting variables in denominators and understanding the factorization process, particularly in the expression \(\frac{x^2 - 25}{12x^2}\) leading to \(\frac{3(x - 5)}{18x^2}\).

PREREQUISITES
  • Understanding of rational expressions and their simplification
  • Familiarity with factoring polynomials, specifically quadratic expressions
  • Knowledge of basic algebraic operations, including multiplication and division of fractions
  • Ability to manipulate algebraic fractions and identify common factors
NEXT STEPS
  • Study polynomial factorization techniques, focusing on quadratic expressions
  • Learn about simplifying rational expressions through common factors
  • Practice multiplying and dividing rational expressions with varying degrees
  • Explore the concept of variable counting in algebraic fractions to avoid common mistakes
USEFUL FOR

Students learning algebra, educators teaching rational expressions, and anyone seeking to improve their skills in simplifying and manipulating algebraic fractions.

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I was wondering if someone could check these questions to make sure that I am doing these correctly. I have attached a few questions in word document as I could not type it properly on here.
 

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[tex]\frac{5x^ 2- 20}{x^2+14x+24}= \frac{5(x^2-4)}{(x+12)(x+2)}[/tex]

x2- 4 can be factored and this simplifies more.

[tex]\(\frac{25}{12x^2y}\)\(\frac{3y^3}{10x}\)= \frac{5y^2}{8x^2}[/tex]

Carefully count the number of 'x's in the denominators.

[tex]\(\frac{x^2-25}{12x^2}\)\(\frac{9x}{2x^2+10x}\)= \frac{3(x-5)}{18x^2}[/tex]

How did the "9" in the numerator become "3"?
 


Hello,

Thank you for reaching out for assistance with your rational expressions questions. We are happy to review your work and provide feedback.

Please attach the word document with the questions so that we can accurately check your work. It is important to provide all necessary information for us to properly review and provide feedback. We will do our best to help you understand and improve your understanding of rational expressions.

Thank you.
 

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