To simplify the fraction \(\frac{x675}{x453}\), we can factor out the common term \(x\).
First, rewrite the fraction:
\[ \frac{x675}{x453} = \frac{675}{453} \]
Next, we simplify \(\frac{675}{453}\) by finding the greatest common divisor (GCD) of 675 and 453.
- Find the GCD:
- The prime factorization of 675 is \(3^3 \times 5^2\).
- The prime factorization of 453 is \(3^2 \times 151\).
The common factor is \(3^2\), which is \(9\).
- Divide both the numerator and the denominator by their GCD (9):
\[ \frac{675 \div 9}{453 \div 9} = \frac{75}{50.333...} \]
Now let's adjust our approach, since we need an integer result in the denominator.
Continuing with the integer division:
Dividing \(453\) leads us to:
\[ \frac{675 \div 3}{453 \div 3} = \frac{225}{151} \]
Now, both \(225\) and \(151\) cannot be simplified further (no common factors greater than 1).
Therefore, the simplified form of the original fraction \(\frac{x675}{x453}\) is:
\[ \frac{225}{151} \]
Thus, the final simplified fraction is:
\[ \frac{225}{151} \]
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