High School

What is the value of the rational expression [tex]\frac{2x+1}{x^2}[/tex] when [tex]x=5[/tex]?

A. [tex]\frac{2}{5}[/tex]
B. [tex]\frac{3}{5}[/tex]
C. [tex]\frac{12}{25}[/tex]
D. [tex]\frac{11}{10}[/tex]

Answer :

To find the value of the rational expression [tex]\(\frac{2x+1}{x^2}\)[/tex] when [tex]\(x=5\)[/tex], let's calculate it step-by-step.

1. Substitute [tex]\(x=5\)[/tex] into the expression.
[tex]\[
\text{Expression: } \frac{2 \cdot 5 + 1}{5^2}
\][/tex]

2. Calculate the numerator.
- Multiply 2 by 5, which gives [tex]\(10\)[/tex].
- Add 1 to [tex]\(10\)[/tex], resulting in [tex]\(11\)[/tex].

3. Calculate the denominator.
- Square 5, which gives [tex]\(25\)[/tex].

4. Divide the numerator by the denominator.
[tex]\[
\frac{11}{25} = 0.44
\][/tex]

The value of the rational expression [tex]\(\frac{2x+1}{x^2}\)[/tex] when [tex]\(x=5\)[/tex] is [tex]\(\frac{11}{25}\)[/tex], which is equivalent to [tex]\(0.44\)[/tex]. Among the given options, [tex]\(\frac{11}{25}\)[/tex] doesn't directly appear, but the decimal 0.44 confirms the value from our calculation.