To simplify the expression [tex]\(\frac{x^2 + 4}{2}\)[/tex], follow these steps:
1. Distribute the denominator to each term in the numerator:
The expression [tex]\(\frac{x^2 + 4}{2}\)[/tex] can be broken down by applying the denominator to each term in the numerator separately. This gives us:
[tex]\[
\frac{x^2}{2} + \frac{4}{2}
\][/tex]
2. Simplify each term:
- For the first term, [tex]\(\frac{x^2}{2}\)[/tex], we simply keep it as it is:
[tex]\[
\frac{x^2}{2}
\][/tex]
- For the second term, [tex]\(\frac{4}{2}\)[/tex], we simplify it:
[tex]\[
\frac{4}{2} = 2
\][/tex]
3. Combine the simplified terms:
Now, put the simplified terms together:
[tex]\[
\frac{x^2}{2} + 2
\][/tex]
Hence, the simplified form of the expression [tex]\(\frac{x^2 + 4}{2}\)[/tex] is:
[tex]\[
\boxed{\frac{x^2}{2} + 2}
\][/tex]
