Rational Expressions (AQA A-Level Mathematics): Flashcards

A function of the form $\frac{p(x)}{q(x)}$ where $p(x)$ and $q(x)$ are polynomials

Use polynomial factorization, then cancel common factors

Numerator degree $\geq$ denominator degree

Perform division first

$\frac{A}{x+a} + \frac{B}{x+b}$

$\frac{B}{x-a} + \frac{C}{(x-a)^2}$

Multiply both sides by common denominator

Use tactical substitution (values that make terms zero)

Same/common denominator

$\equiv$ (identity symbol)