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Answer :
To solve the problem and determine which option is equivalent to the fraction [tex]\(\frac{57 x^{11}}{57 x^{11}}\)[/tex], let's break it down step by step:
1. Understanding the Fraction:
- The given fraction is [tex]\(\frac{57 x^{11}}{57 x^{11}}\)[/tex].
- Here, the same term is both in the numerator and the denominator.
2. Simplifying the Fraction:
- When a term is divided by itself, the result is 1.
- Therefore, the expression [tex]\(\frac{57 x^{11}}{57 x^{11}}\)[/tex] simplifies to 1.
3. Comparing to the Options:
- Option (1) is 1.
- The other options represent expressions with variables and numbers that are not equivalent to 1:
- Option (2) is [tex]\(114 x^{22}\)[/tex].
- Option (3) is [tex]\(57 x^{22}\)[/tex].
- Option (4) is [tex]\(114 x^{121}\)[/tex].
Since the fraction simplifies to 1, the correct answer is option (1) [tex]\(1\)[/tex].
1. Understanding the Fraction:
- The given fraction is [tex]\(\frac{57 x^{11}}{57 x^{11}}\)[/tex].
- Here, the same term is both in the numerator and the denominator.
2. Simplifying the Fraction:
- When a term is divided by itself, the result is 1.
- Therefore, the expression [tex]\(\frac{57 x^{11}}{57 x^{11}}\)[/tex] simplifies to 1.
3. Comparing to the Options:
- Option (1) is 1.
- The other options represent expressions with variables and numbers that are not equivalent to 1:
- Option (2) is [tex]\(114 x^{22}\)[/tex].
- Option (3) is [tex]\(57 x^{22}\)[/tex].
- Option (4) is [tex]\(114 x^{121}\)[/tex].
Since the fraction simplifies to 1, the correct answer is option (1) [tex]\(1\)[/tex].
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