To determine the value of the rational expression [tex]\(\frac{x + 13}{x - 3}\)[/tex] when [tex]\(x\)[/tex] is equal to 7, follow these steps:
1. First, substitute [tex]\(x = 7\)[/tex] into the expression. The expression becomes:
[tex]\[
\frac{7 + 13}{7 - 3}
\][/tex]
2. Next, perform the addition in the numerator:
[tex]\[
7 + 13 = 20
\][/tex]
So the expression is now:
[tex]\[
\frac{20}{7 - 3}
\][/tex]
3. Then, perform the subtraction in the denominator:
[tex]\[
7 - 3 = 4
\][/tex]
Now the expression is:
[tex]\[
\frac{20}{4}
\][/tex]
4. Finally, perform the division:
[tex]\[
\frac{20}{4} = 5
\][/tex]
Therefore, the value of the rational expression [tex]\(\frac{x + 13}{x - 3}\)[/tex] when [tex]\(x = 7\)[/tex] is [tex]\(5\)[/tex].
The correct answer is:
C. 5
