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What is the value of the rational expression below when [tex]$x$[/tex] is equal to 7?

[tex]\frac{x+13}{x-3}[/tex]

A. 20
B. [tex]-\frac{13}{3}[/tex]
C. 5
D. 2


Sagot :

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