Partial Fractions - Practice
Maths: Edexcel A Level Pure Maths, topic 2.8.5
What are Partial Fractions?
If an algebraic fraction has a numerator that is lower in degree than its denominator, we can split it up into partial fractions. This allows us to do calculations more easily.
What are the linear factors in a denominator?
- To split up an algebraic fraction into its partial fractions, we need to factorise the denominator into its linear factors.
- For example,
Fractions with 2 linear factors
- If a fraction has a denominator consisting of 2 different linear factors, we can express it as the sum of partial fractions:
- For example,
- Where and are constants.
- These constants are found by adding the fractions and either substituting in values of or by equating coefficients of .
Fractions with 3 linear factors
- If a fraction has a denominator consisting of 3 different linear factors, we can express it as the sum of partial fractions.
- For example,
- Where , and are constants to be found by substitution or equating coefficients.
Fractions with repeated factors
- If a fraction has a denominator consisting of 2 different linear factors and one is repeated, we can express it as the sum of partial fractions:
- For example,
- Where , and are constants to be found by substitution or equating coefficients.
Test yourself on Partial Fractions - Practice
What is the correct method for splitting the following fraction?