Rational homology of $\Omega^{n+1}\Sigma^{n+1}X$

Question

I want to know how compute, by induction and using the Serre spectral sequence for homology, $H_*(\Omega^{n+1}\Sigma^{n+1}X, \mathbb{Q})$. I know that I have to use the path-loop fibration $$ \Omega^{n+1}\Sigma^{n+1}X \to P\Omega^{n}\Sigma^{n+1}X \to \Omega^{n}\Sigma^{n+1}X $$ Nevertheless I don't know how to make the inductive case, i.e n=1.

Any suggestions? Somebody knows a reference?