To solve the given problem, let's consider the given expression:
[tex]\[
\frac{2 - e^{3x}}{5 e^{3x} + 1}
\][/tex]
Here's the detailed step-by-step simplification of this expression:
1. The numerator of the fraction is [tex]\( 2 - e^{3x} \)[/tex]. This is a simple linear expression involving the exponential function [tex]\( e^{3x} \)[/tex].
2. The denominator of the fraction is [tex]\( 5 e^{3x} + 1 \)[/tex]. This is another linear expression involving the same exponential function [tex]\( e^{3x} \)[/tex].
3. The fraction represents the division of the numerator by the denominator.
So, the simplified form of the given expression is:
[tex]\[
\frac{2 - e^{3x}}{5 e^{3x} + 1}
\][/tex]
This expression cannot be further simplified without additional context or constraints. Thus, the final simplified form of the given problem is:
[tex]\[
\boxed{\frac{2 - e^{3x}}{5 e^{3x} + 1}}
\][/tex]
