To solve the problem of subtracting the two fractions [tex]\(\frac{5}{7}\)[/tex] and [tex]\(\frac{6}{11}\)[/tex], we follow these steps:
1. Find a common denominator: The denominators of the two fractions are 7 and 11. The least common multiple (LCM) of 7 and 11 is [tex]\(77\)[/tex].
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{5}{7}\)[/tex]:
[tex]\[
\frac{5}{7} = \frac{5 \times 11}{7 \times 11} = \frac{55}{77}
\][/tex]
- For [tex]\(\frac{6}{11}\)[/tex]:
[tex]\[
\frac{6}{11} = \frac{6 \times 7}{11 \times 7} = \frac{42}{77}
\][/tex]
3. Subtract the numerators once the denominators are the same:
[tex]\[
\frac{55}{77} - \frac{42}{77} = \frac{55 - 42}{77} = \frac{13}{77}
\][/tex]
Thus, the result of the subtraction [tex]\(\frac{5}{7} - \frac{6}{11}\)[/tex] is [tex]\(\frac{13}{77}\)[/tex]. This fraction is already in its simplest form.
The final answer is:
[tex]\[
\frac{13}{77}
\][/tex]
