The given expression is:

$\frac{e^{x}}{e^{2x} - 5e^{x} + 6}$

To simplify this expression, let's substitute $y = e^x$. This substitution turns the expression into:

$\frac{y}{y^2 - 5y + 6}$

Now, factor the denominator:

$y^2 - 5y + 6 = (y - 2)(y - 3)$

Thus, the expression becomes:

$\frac{y}{(y - 2)(y - 3)}$

Now, substitute back $y = e^x$ to return to the original variable:

$\frac{e^x}{(e^x - 2)(e^x - 3)}$

This is the simplified form of the given expression.

Would you like more details on any steps? Or do you have another question related to this?

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Here are 5 related questions:

1. How do you factor quadratic expressions like $y^2 - 5y + 6$?
2. What is the role of substitution in simplifying expressions like this?
3. How can exponential functions be simplified when their exponents have the same base?
4. Can this kind of expression be simplified further using limits or asymptotic behavior?
5. How would you graph the simplified expression?

Tip: When dealing with exponential functions, substitution can often simplify the problem by converting it into a familiar polynomial form.