Rational Expressions (Edexcel A-Level Mathematics): Flashcards

A function of the form $p(x)/q(x)$ with polynomials.

Use polynomial factorization and cancel common factors.

$f(x) = \frac{x^2 + 5}{x - 8}$ is a rational function.

Write the expression as a sum of simpler fractions.

Perform polynomial long division before finding partial fractions.

Use strategic values of $x$ to simplify the equations.

$\frac{2}{(x+1)(x+3)} = \frac{1}{x+1} - \frac{1}{x+3}$.

$\frac{1}{x^2-1} = \frac{1}{2(x-1)} - \frac{1}{2(x+1)}$.

Use $A/(x-1) + B/(x-1)^2 + C/(x-2)$.

Combine to $\frac{11-x}{(3-x)(1+x)}$.