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We prove that if $G$ is a free-torsion group and $w(t)$ is a word in thealphabet $G \sqcup \{t^{\pm 1}\}$ with exponent sum one, then the group$<G,t|(w(t))^k = 1>$, where $k \geq 2$, is relatively hyperbolic with respectto $G$.

The relative hyperbolicity of one-relator relative presentations