Proof without Words

Partial Fraction Decomposition

Abstract

This short article presents two visual proofs for classical partial fraction identities: one in two dimensions, the other in three. Rather than relying on algebraic manipulation, each diagram uses geometry to convey the decomposition clearly
and intuitively. The visual format invites students to explore the structure of the expressions without getting lost symbolic detail, opening space for meaningful discussion and deeper understanding. These diagrams may also serve as a springboard for students to create their own visual representation of algebraic ideas.