1. Aims: To be able to solve partial fractions with repeated factors To be able to spot and cancel down in improper fraction before splitting it into it’s partial fractions Algebra - Partial Fractions Lesson 4 Plenary on white boards? http://integralmaths.org/resources/file.php/41/js/AlgPartialFrac.tst

2. Denominators with a repeated linear factor In this case, the partial fractions will be of the form: This is an example of a fraction whose denominator contains a repeated linear factor. Suppose we wish to express in partial fractions. We can now find A, B and C using a combination of substitution and equating the coefficients.

3. To find B we can switch to the method of comparing coefficients. Substitute x = into : 1 1 Denominators with a repeated linear factor Multiply through by (x + 4)(x – 3) 2 1

4. Therefore Express as a sum of partial fractions. Let Equate the coefficients of x 2 in : 1 Denominators with a repeated linear factor

5. Multiply through by x 2 (4 – x ): Substitute x = into : 1 1 1 Denominators with a repeated linear factor

6. We can find A by comparing the coefficients of x 2. Therefore Denominators with a repeated linear factor

7. On w/b express as P.F. Do exercise 1 on the worksheet 15 mins

8. Improper fractions Remember, an algebraic fraction is called an improper fraction if the degree of the polynomial is equal to, or greater than, the degree of the denominator. To express an improper fraction in partial fractions we start by expressing it in the algebraic equivalent of mixed number form. Express in partial fractions. Using long division:

9. Improper fractions Therefore

10. On w/b 1. Do exercise 2 on worksheet.