13.07 Algebraic fractions with factorisation (Extended)
Factorisation and simplification
It is generally a good idea to simplify all fractions where possible before proceeding with any operation (addition, subtraction, multiplication or division). This is particularly important when we are dealing with algebraic fractions that involve binomial or quadratic expressions, as cancelling common factors can make these seemingly complicated expressions much easier to work with. We may need to use any or all of the factorising techniques from the previous lesson, so make sure you are familiar with them all. It is accepted practice to present final answers in factorised form.
Practice question
Question 1
Simplify the rational expression $\frac{2r-8}{r^2-16}$2r−8r2−16
Multiplication of algebraic fractions
To multiply algebraic fractions, we multiply numerators together to form the new numerator, and denominators together to form the new denominator. We also want to check for common factors that can be cancelled.
Practice question
Question 2
Simplify the following expression:
$\frac{p+7}{5}\times\frac{5p-2}{p^2+14p+49}$p+75×5p−2p2+14p+49
Division of algebraic fractions
Dividing by an algebraic fraction is the same as multiplying by the reciprocal.
Practice question
Question 3
Simplify $\frac{k-1}{20}\div\frac{k^2-10k+9}{4}$k−120÷k2−10k+94.