Algebraic Fractions

Simplifying Algebraic Fractions

  • An algebraic fraction is simply a fraction where the numerator (top number) and/or the denominator (bottom number) are algebraic expressions.
  • Simplification of algebraic fractions involves factoring the numerator and the denominator, and then cancelling common factors.

Example

  • Consider 2x^2 / 4x. Here, both the numerator and the denominator can be factored to 2*x*x / 2*2*x
  • The common factors 2 and x can be cancelled resulting in x / 2

Addition and Subtraction of Algebraic Fractions

  • When adding or subtracting algebraic fractions, remember the need for a common denominator.
  • If fractions have the same denominator, simply add or subtract the numerators.

Example

  • If we have x / y + z / y, the result would be (x + z) / y

Multiplication and Division of Algebraic Fractions

  • When multiplying algebraic fractions, multiply the numerators together for the new numerator and multiply the denominators together for the new denominator.
  • Dividing algebraic fractions is just like dividing normal fractions. Keep the first term the same, change the division sign to a multiplication sign, and flip the second fraction.

Example

  • For multiplication, a / b * c / d gives (a * c) / (b * d)
  • For division, (a / b) / (c / d) changes to (a / b) * (d / c)