Simplifying Algebraic Fractions

Simplifying Algebraic Fractionsvideo

Simplifying algebraic fractions

What is an algebraic fraction?

• An algebraic fraction is a fraction with an algebraic expression on the top (numerator) and/or the bottom (denominator)

How do you simplify an algebraic fraction?

• If possible, factorise fully the top and bottom

  • E.g. $\frac{2x}{x^2+3x}=\frac{2x}{x\left(x+3\right)}$

• Cancel common factors

  • This factor may be a single term

    • E.g. $\frac{\cancel{x}\left(5x-1\right)}{4\cancel{x}}=\frac{5x-1}{4}$

  • It could also be a common bracket

    • E.g. $\frac{x\cancel{\left(x+2\right)}}{\cancel{\left(x+2\right)}\left(x-1\right)}=\frac{x}{x-1}$

• A common mistake is to cancel a factor that is not common to all terms in either the top or the bottom of a fraction

  • E.g. The fraction $\frac{6x}{x+1}$ cannot be simplified

    • $x$ is not common to all terms in the bottom of the fraction

    • and the expression on the bottom cannot be factorised