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All 9 lessons in Algebraic Fractions

  1. 1. Simplifying Algebraic Fractions I — Cancelling Common Monomial Factors

    Find the HCF of two monomials and simplify an algebraic fraction by cancelling a common monomial factor, handling signs and restrictions.

  2. 2. Simplifying Algebraic Fractions II — Factorising Polynomials, and Undefined Fractions

    Simplify fractions by factorising polynomial numerators and denominators, and find the values for which a fraction is undefined.

  3. 3. Adding and Subtracting Algebraic Fractions I — Common and Simple Denominators

    Add and subtract algebraic fractions with like denominators, find the LCD for monomial and simple linear denominators, and handle subtraction signs.

  4. 4. Adding and Subtracting Algebraic Fractions II — Polynomial Denominators

    Factorise polynomial denominators to build the LCD from distinct factors, then combine and simplify fractions with polynomial denominators.

  5. 5. Multiplying Algebraic Fractions

    Multiply algebraic fractions by factorising fully and cross-cancelling matching factors across numerators and denominators.

  6. 6. Dividing Algebraic Fractions and Mixed Operations

    Divide algebraic fractions by inverting and multiplying, simplify complex fractions, and process chains of multiplication and division.

  7. 7. Equations Involving Algebraic Fractions

    Solve equations with fractions by multiplying through by the LCD, solve the resulting polynomial, and reject extraneous solutions.

  8. 8. Substitution in Algebraic Fractions

    Evaluate algebraic fractions by direct substitution, by ratio substitution with a parameter k, and by substituting an algebraic relationship.

  9. 9. Simultaneous Equations Involving Algebraic Fractions

    Clear fractions from a simultaneous system by multiplying each equation by its LCD, solve the standard system, and use a change of variable when unknowns sit in denominators.

Unit code SSA11