Certainly! Let's solve the problem step-by-step.
Consider a number [tex]\( a \)[/tex] such that [tex]\( 0 < a < 1 \)[/tex]. We want to calculate the value of the expression [tex]\( a + \frac{1}{a} \)[/tex].
### Step-by-Step Solution:
1. Understand the Constraints: Given the constraint [tex]\( 0 < a < 1 \)[/tex], [tex]\( a \)[/tex] is a positive number but less than 1.
2. Select a Specific Value for [tex]\( a \)[/tex]: To find a clear numeric answer, we can choose a specific value for [tex]\( a \)[/tex] that fits the constraint [tex]\( 0 < a < 1 \)[/tex].
Let's select [tex]\( a = 0.5 \)[/tex], which satisfies [tex]\( 0 < 0.5 < 1 \)[/tex].
3. Substitute [tex]\( a \)[/tex] into the Expression: With [tex]\( a = 0.5 \)[/tex], substitute this value into the expression [tex]\( a + \frac{1}{a} \)[/tex]:
[tex]\[
a + \frac{1}{a} = 0.5 + \frac{1}{0.5}
\][/tex]
4. Calculate the Reciprocal: Calculate the reciprocal of [tex]\( a \)[/tex]:
[tex]\[
\frac{1}{0.5} = 2
\][/tex]
5. Simplify the Expression: Now, add [tex]\( a \)[/tex] and its reciprocal:
[tex]\[
0.5 + 2 = 2.5
\][/tex]
### Conclusion:
Thus, when [tex]\( a = 0.5 \)[/tex] (which is within the given range [tex]\( 0 < a < 1 \)[/tex]), the value of the expression [tex]\( a + \frac{1}{a} \)[/tex] is [tex]\( 2.5 \)[/tex].
