Single example with detailed solution for rationalising a binomial denominator which contains surds.

Adapted from 'Surds: rationalising the denominator conjugate' by Ben Brawn.

Simple example with detailed solution for rationalising a single-term, surd denominator.

Adapted from 'Surds: rationalising the denominator simple' by Ben Brawn.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Adding several rational functions.

Finding the numerators & denominators of 4 equivalent fractions.

8/9/15

Practice of cancelling a fraction, where the denominator will reduce to either 5,10, 20, 25, or 50 and then multiplying numerator and denominator by either 20, 10, 5, 4 or 2 respectively, to represent the fraction as a percentage.  A helpful strategy in the QTS test...

Tweaked the variables to avoid duplicate fractions in the 2 parts & make the second slightly more tricky, on average.  Used the Testing facility to prevent 100 or 200 appearing in the denominators.

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Cancel fractions where the numerator and denominator are both factorials.