Start by identifying the rational expression to simplify: \(\frac{x^2 + 5x + 6}{x^2 + 7x + 10}\).
Factor both the numerator and the denominator. For the numerator \(x^2 + 5x + 6\), find two numbers that multiply to 6 and add to 5, then write it as \((x + a)(x + b)\).
Similarly, factor the denominator \(x^2 + 7x + 10\) by finding two numbers that multiply to 10 and add to 7, then write it as \((x + c)(x + d)\).
Rewrite the original expression using the factored forms: \(\frac{(x + a)(x + b)}{(x + c)(x + d)}\).
Look for any common factors in the numerator and denominator and cancel them out to simplify the expression.