To solve the expression [tex]\(\frac{x + y + 1}{x + y}\)[/tex], let's break it down step by step.
First, we recognize that the expression in the denominator, [tex]\(x + y\)[/tex], is not zero (i.e., [tex]\(x + y \neq 0\)[/tex]) to avoid division by zero.
Given the expression:
[tex]\[
\frac{x + y + 1}{x + y}
\][/tex]
we can split the fraction into two parts:
[tex]\[
\frac{x + y + 1}{x + y} = \frac{x + y}{x + y} + \frac{1}{x + y}
\][/tex]
Now, let's simplify each part of this sum:
1. [tex]\(\frac{x + y}{x + y}\)[/tex]:
[tex]\[
\frac{x + y}{x + y} = 1
\][/tex]
(as long as [tex]\(x + y \neq 0\)[/tex]).
2. [tex]\(\frac{1}{x + y}\)[/tex] remains as it is.
Therefore, we can combine these results to get:
[tex]\[
\frac{x+y+1}{x+y} = 1 + \frac{1}{x+y}
\][/tex]
So, the final simplified answer to the expression [tex]\(\frac{x + y + 1}{x + y}\)[/tex] is:
[tex]\[
1 + \frac{1}{x + y}
\][/tex]
