Algebraic Fractions Demystified: Simplify Now 1

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Monic expressions are polynomials where the coefficient of the highest degree term is 1.

Here's the process for simplifying algebraic fractions with monic expressions:

Factor both the numerator and denominator into quadratic expressions.
Simplify the fraction by cancelling out the common terms.
Example: Simplify the fraction (x^2 + 5x + 6) / (x^2 + 3x + 2)

Factor both the numerator and denominator into quadratic expressions:
(x^2 + 5x + 6) = (x + 2)(x + 3)
(x^2 + 3x + 2) = (x + 1)(x + 2)
Simplify the fraction by cancelling out the common terms:
(x^2 + 5x + 6) / (x^2 + 3x + 2) = (x + 2)(x + 3) / (x + 1)(x + 2) = (x + 3) / (x + 1)
And that's it! By using quadratic factorization, the fraction has been simplified.