Proof in vector analysis

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Given $\mathbf{x}$^$\mathbf{a}$=$\mathbf{b-x}$

Prove

$(a^2+1)\mathbf{x}=\mathbf{a}$^$\mathbf{b+b(a.b)a}$

I have been using this same dot product and crossproduct method, but don't get it.

The method I used is similar to a question that I recently posted here.