Question

simpllify the fraction x675 over x453

Answer 1

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.

1. **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 \(9\).

2. **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:

\[
\frac{225}{151}
\]