Rational Expressions Answers: Check Your Work

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The discussion revolves around checking the accuracy of solutions for various rational expressions. A user requests feedback on their work, providing specific expressions for review. Key points include the factoring of expressions, careful counting of variables in denominators, and clarifying how numerical values in expressions change during simplification. Participants emphasize the importance of attaching documents for precise feedback. The conversation highlights a collaborative effort to enhance understanding of rational expressions.
shorty_47_2000
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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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\frac{5x^ 2- 20}{x^2+14x+24}= \frac{5(x^2-4)}{(x+12)(x+2)}

x2- 4 can be factored and this simplifies more.

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

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

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

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.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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