Sure! Let's solve the given expression step-by-step:
We need to evaluate and simplify the expression:
[tex]\[
\frac{1-6}{6} + \frac{n+6}{8}
\][/tex]
1. Calculate the first fraction:
[tex]\[
\frac{1-6}{6} = \frac{-5}{6} = -0.8333333333333334
\][/tex]
So, the first fraction is [tex]\(-0.8333333333333334\)[/tex].
2. Calculate the second fraction:
Since [tex]\(n\)[/tex] is a variable, we leave it in the fractional form:
[tex]\[
\frac{n+6}{8}
\][/tex]
This can be written as:
[tex]\[
\frac{n}{8} + \frac{6}{8} = \frac{n}{8} + \frac{3}{4}
\][/tex]
Thus, the second fraction is [tex]\(\frac{n}{8} + \frac{3}{4}\)[/tex].
3. Add the fractions together:
Combine the first fraction and the second fraction:
[tex]\[
-0.8333333333333334 + \left(\frac{n}{8} + \frac{3}{4}\right)
\][/tex]
Combine the constant terms:
[tex]\[
-0.8333333333333334 + \frac{3}{4}
\][/tex]
Convert [tex]\(\frac{3}{4}\)[/tex] to a decimal to make the addition easier:
[tex]\[
-0.8333333333333334 + 0.75 = -0.0833333333333334
\][/tex]
Combine this with the remaining variable term:
[tex]\[
\frac{n}{8} - 0.0833333333333334
\][/tex]
Therefore, the final combined result is:
[tex]\[
\frac{n}{8} - 0.0833333333333334
\][/tex]
To summarize, the individual parts are:
[tex]\[
\text{First fraction:} \ -0.8333333333333334
\][/tex]
[tex]\[
\text{Second fraction:} \ \frac{n}{8} + \frac{3}{4}
\][/tex]
[tex]\[
\text{Final result:} \ \frac{n}{8} - 0.0833333333333334
\][/tex]
