Equivalence and Rational Functions in MYP Year 5 Standard Maths

What Are Rational Functions?

A rational function is any function that can be written as the ratio of two polynomials — for example, (x² − 1)/(x + 1). The study of rational functions in MYP Year 5 Standard focuses on recognising equivalent forms, simplifying expressions, and understanding where rational expressions are undefined.

Simplifying Rational Expressions

To simplify a rational expression, factorise both the numerator and denominator, then cancel any common factors. For instance:

(x² − 1)/(x + 1) = (x + 1)(x − 1)/(x + 1) = x − 1, provided x ≠ −1

The restriction x ≠ −1 is important — students must state the values for which the original expression is undefined.

Equivalent Forms

Two rational expressions are equivalent if one can be transformed into the other through valid algebraic steps. Recognising equivalence is useful when comparing solutions, checking answers, or choosing the most useful form for a given purpose.

Adding and Subtracting Rational Expressions

Combining rational expressions requires finding a common denominator — the same process as adding ordinary fractions, applied to algebraic terms. Students must be comfortable with factorising denominators before finding the lowest common denominator.

Where Rational Expressions Break Down

Students must identify values of the variable that make the denominator equal to zero. These are excluded from the domain. This connects to the graphical behaviour of rational functions — asymptotes occur at these excluded values.

Assessment Connection

Criterion A tasks may ask students to simplify, compare, or operate with rational expressions. Criterion B (Investigating Patterns) may involve exploring how different forms of a rational expression relate graphically. Precision in stating domain restrictions is often rewarded in communication marks.