Methyl tert-butyl ether (MTBE) has received high attention since it contributed to cleaner air but adversely contaminated thousands of underground storage tank sites. Because MTBE is very soluble in water, it is difficult to remove from solution by conventional remediation techniques, therefore, biodegradation of MTBE has become a remediation alternative. In order to understand the transport and transformation processes, in this paper, we present a closed form analytical solution, which can be applied as a screening tool. The possible reaction pathways of first-order reactions are described as a reaction matrix. The singular value decomposition is conducted analytically to decouple the partial differential equations of the multi-species transport system coupled by the reaction matrix into multiple independent subsystems. Therefore, the complexity of mathematical description for the reactive transport system is significantly reduced and the analytical expressions can be derived.