Algebraic Fractions
Algebraic fractions extend fraction skills to expressions with pronumerals, requiring careful attention to common denominators and restrictions on variables.
What You Need to Know
Key Concept Diagram
Simplify algebraic fractions by factorising numerator and denominator then cancelling common factors
Add and subtract algebraic fractions by finding the lowest common denominator (LCD)
Multiply algebraic fractions by multiplying numerators and denominators separately after cancelling
Identify restrictions: values of the variable that make a denominator equal zero must be excluded
Key Vocabulary
Algebraic fraction
A fraction whose numerator or denominator (or both) contain algebraic expressions
Lowest Common Denominator
The smallest expression that is a multiple of every denominator in a set of fractions
Restriction
A value of the variable for which a denominator becomes zero, making the expression undefined
Factorisation
Rewriting an expression as a product of its factors to allow cancellation in fractions
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Simplify: (x² - 9) / (x + 3)
Question 2
Add: 2/x + 3/(x+1). What is the correct numerator over the LCD x(x+1)?
Question 3
Which value of x must be excluded from (2x)/(x² - 4)?
Key Concepts Summary
- ●Simplify algebraic fractions by factorising numerator and denominator then cancelling common factors
- ●Add and subtract algebraic fractions by finding the lowest common denominator (LCD)
- ●Multiply algebraic fractions by multiplying numerators and denominators separately after cancelling
- ●Identify restrictions: values of the variable that make a denominator equal zero must be excluded