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I am having difficulty symbolically resolving the LHS of this identity algebraically:

[itex]\frac{r}{2} \left[ \left(8 \pi P(r) + \frac{1}{r^2} \right) \frac{r}{r - 2u} - \frac{1}{r^2} \right] = \frac{4 \pi r^3 P(r) + u}{r(r - 2u)}[/itex]

[itex] \left(4 \pi r P(r) + \frac{1}{2r} \right) \frac{r}{r - 2u} - \frac{1}{2r} = \frac{4 \pi r^3 P(r) + u}{r(r - 2u)}[/itex]

[itex] \left( 4 \pi r^2 P(r) + \frac{1}{2} \right) \frac{1}{r - 2u} - \frac{1}{2r} = \frac{4 \pi r^3 P(r) + u}{r(r - 2u)}[/itex]

[itex]\frac{4 \pi r^2 P(r)}{r-2 u}+\frac{1}{2 (r-2 u)}-\frac{1}{2 r} = \frac{4 \pi r^3 P(r) + u}{r(r - 2u)}[/itex]

Any collaboration would be greatly appreciated.

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# Symbolic proof of identity

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