Algebraic Fractions Demystified: Simplify Now 4

📢 Receive Free Study Resources and Special Offers 🧲

To simplify algebraic fractions with non-monic expressions by quadratic factorization, you need to factor the numerator and denominator of the fraction into simpler expressions.

Here's the process:

Factor the numerator and denominator into quadratic expressions.
Use the common factor(s) from the numerator and denominator to cancel out terms.
Simplify the fraction by dividing the remaining expression in the numerator by the expression in the denominator.
Example: Simplify the fraction (2x^2 + 7x + 3)/(x^2 + 5x + 6)

Factor both numerator and denominator:
(2x^2 + 7x + 3) = (2x + 1)(x + 3)
(x^2 + 5x + 6) = (x + 2)(x + 3)
Use the common factor(s) to cancel out terms:
(2x + 1)(x + 3) / (x + 2)(x + 3) = (2x + 1) / (x + 2)
Simplify the fraction:
(2x + 1) / (x + 2)