To express the sum [tex]\(\frac{x}{x+5} + \frac{5}{x+5}\)[/tex] in its simplest form, we need to combine the two fractions since they have the same denominator.
Given the expression:
[tex]\[
\frac{x}{x+5} + \frac{5}{x+5}
\][/tex]
Step 1: Combine the numerators over the common denominator.
The fractions share the same denominator [tex]\((x+5)\)[/tex], so we can add the numerators directly:
[tex]\[
\frac{x + 5}{x+5}
\][/tex]
Step 2: Simplify the fraction.
Notice that both the numerator and denominator contain the term [tex]\((x+5)\)[/tex]:
[tex]\[
\frac{x+5}{x+5} = 1
\][/tex]
Thus, the simplified form of the expression [tex]\(\frac{x}{x+5} + \frac{5}{x+5}\)[/tex] is:
[tex]\[
\boxed{1}
\][/tex]
So the correct answer is [tex]\(D\)[/tex].
