tricky completing the square

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$$\frac{4k_{0}p_{1}+p_{0}\left ( k_{0}^{2}-2k_{0}k_{1}+k_{1}^{2} \right )}{\left ( k_{0}+k_{1} \right )^{2}p_{0}}$$

I need to show that this is equal to $1$ but for my life I can't figure how to arrive at one despite multiple attempts at completing the square. This is an assignment in Quantum mechanics so obviously the focus is not completing the square. But I'd like to see how to arrive at one and the trick(s) involved.

Thanks in advance.