Rational Expressions Answers: Check Your Work

In summary, rational expressions are fractions with polynomials in the numerator and denominator, which can also include variables and exponents. To simplify them, factor both the numerator and denominator and cancel out common factors. A common mistake is forgetting to factor completely. To check your work, plug in the simplified expression for the original variables or use a calculator. Rational expressions can have restrictions, such as a variable in the denominator causing the expression to be undefined, so it is important to check for and exclude these restrictions from the final simplified expression.
  • #1
shorty_47_2000
9
0
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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  • #2
[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"?
 
  • #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.
 

Related to Rational Expressions Answers: Check Your Work

1. What are rational expressions?

Rational expressions are expressions that involve fractions with polynomials in the numerator and denominator. They can also include variables and exponents.

2. How do I simplify rational expressions?

To simplify rational expressions, factor both the numerator and denominator and then cancel out any common factors. You can also use the rules of exponents to simplify expressions with exponents.

3. What is a common mistake when simplifying rational expressions?

A common mistake when simplifying rational expressions is forgetting to factor completely. It is important to factor completely in order to cancel out all common factors and simplify the expression as much as possible.

4. How do I check my work for rational expressions?

To check your work for rational expressions, plug in your simplified expression for the original variables and see if the resulting fractions are equivalent. You can also use a calculator to evaluate both expressions and compare the results.

5. Can rational expressions have restrictions?

Yes, rational expressions can have restrictions. These restrictions occur when a variable in the denominator has a value that would make the expression undefined, such as a division by zero. It is important to check for these restrictions and exclude them from the final simplified expression.

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