To solve the expression [tex]\(\frac{8}{11} - \frac{6}{11} + \frac{3}{11}\)[/tex], follow these steps:
1. Identify the common denominator:
All three fractions have the same denominator, which is 11. This makes the calculation straightforward since we can directly add and subtract the numerators.
2. Perform the operations on the numerators:
First, subtract the numerator of the second fraction from the numerator of the first fraction:
[tex]\[
8 - 6 = 2
\][/tex]
Next, add the numerator of the third fraction to the result:
[tex]\[
2 + 3 = 5
\][/tex]
3. Construct the resulting fraction:
The numerator after performing the operations is 5, and the common denominator remains 11. Therefore, we have:
[tex]\[
\frac{5}{11}
\][/tex]
4. Simplify the fraction (if needed):
The fraction [tex]\(\frac{5}{11}\)[/tex] is already in its simplest form because 5 and 11 are both prime numbers and do not share any common factors other than 1.
Therefore, the simplified result of the expression [tex]\(\frac{8}{11} - \frac{6}{11} + \frac{3}{11}\)[/tex] is:
[tex]\[
\boxed{\frac{5}{11}}
\][/tex]
