Let's break down the given problem step-by-step to simplify the expression:
Given expressions:
[tex]\[
\frac{x+3}{x-8} + \frac{6x-7}{x-8}
\][/tex]
Since the denominators are the same, we can directly add the numerators:
[tex]\[
\frac{(x+3) + (6x-7)}{x-8}
\][/tex]
Next, combine the terms in the numerator:
[tex]\[
(x + 3) + (6x - 7) = x + 3 + 6x - 7 = 7x - 4
\][/tex]
So the expression simplifies to:
[tex]\[
\frac{7x - 4}{x-8}
\][/tex]
This is already in its simplest form as the numerator \(7x - 4\) cannot be factored further to cancel with the denominator \(x - 8\).
Our final simplified result is:
[tex]\[
\frac{7x - 4}{x-8}
\][/tex]
