Self-supervised learning (SSL) has reduced the reliance on expensive labeling in speech technologies by learning meaningful representations from unannotated data. Since most SSL-based downstream tasks prioritize content information in speech, ideal representations should disentangle content from unwanted variations like speaker characteristics in the SSL representations. However, removing speaker information often degrades other speech components, and existing methods either fail to fully disentangle speaker identity or require resource-intensive models. In this paper, we propose a novel disentanglement method that linearly decomposes SSL representations into speaker-specific and speaker-independent components, effectively generating speaker disentangled representations. Comprehensive experiments show that our approach achieves speaker independence and as such, when applied to content-driven tasks such as voice conversion, our representations yield significant improvements over state-of-the-art methods.