5/87-9/65

To subtract the fractions \( \frac{5}{87} - \frac{9}{65} \), we first need to find a common denominator.

The least common multiple (LCM) of 87 and 65 can be calculated as follows:

• The prime factorization of 87 is \( 3 \times 29 \).
• The prime factorization of 65 is \( 5 \times 13 \).

The LCM of 87 and 65 is:

\[ 3 \times 29 \times 5 \times 13 = 1685. \]

Now we can convert each fraction to have this common denominator:

1. For \( \frac{5}{87} \): \[ \frac{5}{87} = \frac{5 \times 65}{87 \times 65} = \frac{325}{1685}. \]

2. For \( \frac{9}{65} \): \[ \frac{9}{65} = \frac{9 \times 87}{65 \times 87} = \frac{783}{1685}. \]

Now we can perform the subtraction: \[ \frac{325}{1685} - \frac{783}{1685} = \frac{325 - 783}{1685} = \frac{-458}{1685}. \]

Thus, the result of \( \frac{5}{87} - \frac{9}{65} \) is: \[ \frac{-458}{1685}. \]