(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hey I need to rearrange the following, and find x in terms of G, M, m, r

[tex]\frac{{GM}}{{x^2 }} = \frac{{Gm}}{{\left( {r - x} \right)^2 }}[/tex]

2. The attempt at a solution

I haven't manged to get far with this problem as I am confused about the powers of x and how to manage them. This is where I have manged to get to:

[tex]

\begin{array}{c}

\frac{{GM}}{{x^2 }} = \frac{{Gm}}{{\left( {r - x} \right)^2 }} \\

x^2 \left( {r - x} \right)^2 = GM\left( {Gm} \right) \\

x^2 \left( {r^2 - 2rx + x^2 } \right) = G^2 Mm \\

r^2 x^2 - 2rx^3 + x^4 = G^2 Mm \\

\end{array}

[/tex]

Any help is greatly appreciated, many thanks in advance,

unique_pavadrin

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# Algebraic Manipulation

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