6.3: Addition and subtraction of algebraic fractions

1) Lesson Objectives:

You should be able to

• simplify algebraic fractions linked by addition and subtraction

Always look through all examples in textbook before lesson.

Steps to simplify addition and subtraction of algebraic fraction:

Steps to simplifying algebraic fractions:

1. Check to see if you can factorise each term's denominator.

Types of factorisation methods :

• Taking out common factors [Ensure that ALL terms have common factors base on coefficient and variables]

• Grouping [Usually 4 terms and u must pair the terms in 2 brackets linked by plus sign]

• Cross Multiplication Method [Terms with variables that has highest power 2 ie: Quadratic]

• Difference of two squares [Two square terms that are linked by minus sign]

2. Find common denominator and combine all fractions into one single fraction.

3. To multiply numerator with the missing factor from the common denominator.

4. Expand numerator and simplify. DO NOT expand the denominator.

5. Check if the numerator can be factorised. If it can factorised, you must factorise.

6. Check if you can cancel common factors form both numerator and denominator. If there is you must cancel common denominator to make the fraction into it's simplest form.

NOTE: Condition for cancelling common factors or common brackets.

• Common factors and common brackets MUST be linked by either multiplication or division in order to be cancelled.

• You cannot cancel common factors or common brackets linked by + or -. Unless it is a common bracket.

• Common factors or common brackets must cancel one from numerator and one from denominator.

• You cannot cancel common factor or common brackets that is from numerator with numerator or denominator with denominator.