Simplifying algebraic fractions

Task goals

• Simplify a monomial fraction by cancelling a common numeric factor from the numerator and denominator.
• Simplify a monomial fraction by cancelling common variable factors between the numerator and denominator, and state the value that makes it undefined.
• Simplify a fraction by factorising a common factor out of a binomial numerator before cancelling it against the denominator.
• Simplify a fraction by factorising both the numerator and denominator, including differences of two squares and quadratic trinomials, cancelling the shared factor, and stating any restrictions on the variable.
• Identify and correct an incorrect simplification of an algebraic fraction, explaining the error.
• Multiply or divide two algebraic fractions and simplify the result.
• Add or subtract two algebraic fractions that share a common denominator.
• Add or subtract two algebraic fractions with different denominators, factorising first where needed, and state any restrictions on the variable.