Let's solve the expression [tex]\(\frac{2-(5+1)}{6^2+4}\)[/tex] step by step.
1. Calculate the numerator:
The numerator is [tex]\(2 - (5 + 1)\)[/tex].
First, compute the expression inside the parentheses: [tex]\(5 + 1 = 6\)[/tex].
Then, subtract this result from 2: [tex]\(2 - 6 = -4\)[/tex].
Hence, the numerator is [tex]\(-4\)[/tex].
2. Calculate the denominator:
The denominator is [tex]\(6^2 + 4\)[/tex].
First, compute the square of 6: [tex]\(6^2 = 36\)[/tex].
Then, add 4 to this result: [tex]\(36 + 4 = 40\)[/tex].
Hence, the denominator is [tex]\(40\)[/tex].
3. Divide the numerator by the denominator:
Now we divide the numerator by the denominator: [tex]\(\frac{-4}{40}\)[/tex].
Simplifying this fraction, we get [tex]\(-0.1\)[/tex].
So, the detailed solution is:
[tex]\[
\frac{2-(5+1)}{6^2+4} = \frac{-4}{40} = -0.1
\][/tex]
Therefore, the final result is [tex]\(\boxed{-0.1}\)[/tex].
