Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Which expression will simplify to 1? Assume [tex]m \neq 9[/tex] and [tex]m \neq -9[/tex].

A. [tex]\left(\frac{m+9}{m-9}\right)\left(\frac{m+9}{m-9}\right)[/tex]

B. [tex]\left(\frac{m+9}{m-9}\right)\left(\frac{m-9}{m+9}\right)[/tex]

C. [tex]\left(\frac{m+9}{m-9}\right)\left(\frac{9+m}{9-m}\right)[/tex]

D. [tex]\left(\frac{m+9}{m-9}\right)\left(\frac{9-m}{9+m}\right)[/tex]

Sagot :

GinnyAnswer
To determine which of the given expressions simplifies to [tex]\(1\)[/tex], we'll analyze each one step-by-step.

Given:

1. [tex]\(\left(\frac{m+9}{m-9}\right)\left(\frac{m+9}{m-9}\right)\)[/tex]
2. [tex]\(\left(\frac{m+9}{m-9}\right)\left(\frac{m-9}{m+9}\right)\)[/tex]
3. [tex]\(\left(\frac{m+9}{m-9}\right)\left(\frac{9+m}{9-m}\right)\)[/tex]
4. [tex]\(\left(\frac{m+9}{m-9}\right)\left(\frac{9-m}{9+m}\right)\)[/tex]

### Expression 1:
[tex]\[ \left(\frac{m+9}{m-9}\right) \left(\frac{m+9}{m-9}\right) \][/tex]
Multiply the fractions directly:
[tex]\[ \frac{(m+9)(m+9)}{(m-9)(m-9)} = \frac{(m+9)^2}{(m-9)^2} \][/tex]
This expression simplifies to [tex]\(\frac{(m+9)^2}{(m-9)^2}\)[/tex], which is not equal to [tex]\(1\)[/tex].

### Expression 2:
[tex]\[ \left(\frac{m+9}{m-9}\right) \left(\frac{m-9}{m+9}\right) \][/tex]
Multiply the fractions directly:
[tex]\[ \frac{(m+9)(m-9)}{(m-9)(m+9)} = \frac{(m+9)(m-9)}{(m+9)(m-9)} = 1 \][/tex]
This expression simplifies to [tex]\(1\)[/tex].

### Expression 3:
[tex]\[ \left(\frac{m+9}{m-9}\right) \left(\frac{9+m}{9-m}\right) \][/tex]
Simplify the second term:
[tex]\[ \frac{9+m}{9-m} = \frac{m+9}{-(m-9)} = -\frac{m+9}{m-9} \][/tex]
Now multiply the fractions:
[tex]\[ \left(\frac{m+9}{m-9}\right) \left(-\frac{m+9}{m-9}\right) = -\frac{(m+9)(m+9)}{(m-9)(m-9)} = -\frac{(m+9)^2}{(m-9)^2} \][/tex]
This expression simplifies to [tex]\(-\frac{(m+9)^2}{(m-9)^2}\)[/tex], which is not equal to [tex]\(1\)[/tex].

### Expression 4:
[tex]\[ \left(\frac{m+9}{m-9}\right) \left(\frac{9-m}{9+m}\right) \][/tex]
Simplify the second term:
[tex]\[ \frac{9-m}{9+m} = -\frac{m-9}{m+9} \][/tex]
Now multiply the fractions:
[tex]\[ \left(\frac{m+9}{m-9}\right) \left(-\frac{m-9}{m+9}\right) = -\frac{(m+9)(m-9)}{(m-9)(m+9)} = -1 \][/tex]
This expression simplifies to [tex]\(-1\)[/tex], which is not equal to [tex]\(1\)[/tex].

Thus, after evaluating all the expressions, the one that simplifies to [tex]\(1\)[/tex] is:

[tex]\[ \left( \frac{m+9}{m-9} \right) \left( \frac{m-9}{m+9} \right) \][/tex]
So, the correct answer is the second expression:
[tex]\[ \left(\frac{m+9}{m-9}\right)\left(\frac{m-9}{m+9}\right) \][/tex]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.