Simplifying algebraic fractions

Introduction to Simplifying Algebraic Fractions

  • An algebraic fraction is a fraction in which the numerator and/or the denominator are algebraic expressions.
  • The concept of simplifying algebraic fractions involves breaking complex expressions down into more simple and manageable parts.
  • Simplifying algebraic fractions works much the same way as simplifying numerical fractions, involving techniques such as finding common factors and cancelling them out.

Methods for Simplifying Algebraic Fractions

  • Factorising both the numerator and the denominator can often aid in simplifying algebraic fractions. For example, if an algebraic fraction has x² - 3x + 2 in the numerator, this can be factorised to (x - 1)(x - 2).
  • Once both the numerator and denominator are factorised, any common factors can be cancelled out to simplify the fraction.
  • Sometimes, it may be necessary to multiply or divide the entire fraction (both the numerator and the denominator) by the same number or expression to simplify. This does not change the value of the fraction.
  • Particularly tricky fractions may require multiple steps or techniques to simplify fully.

Examples of Simplifying Algebraic Fractions

  • Given the algebraic fraction 6x²/12x, we can first simplify by dividing both parts of the fraction by the common factor of 6x, giving us x/2.
  • In the example of (x² - 5x + 6)/(x² - 3x +2 ), this simplifies to (x-2)(x-3)/(x-2)(x-1). Because x - 2 is a common factor, it can be cancelled out from the numerator and denominator, simplifying the fraction to (x - 3)/(x - 1).

Applications of Simplifying Algebraic Fractions

  • Simplifying algebraic fractions has many practical applications in the real world, particularly in fields such as physics, engineering, and economics, where varying quantities are often modelled using algebraic equations.

Extra Points

  • Do not worry if an algebraic fraction looks complicated at first. Break down the numerator and denominator into their factors, cancel out any common factors, and remember to fully simplify to get your answer.
  • Practice is key to becoming proficient at simplifying algebraic fractions. The more fractions you simplify, the better you will get at identifying the necessary steps quickly and accurately.