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Math·Advanced Math·Equivalent expressions

hard

$\frac{46}{p}=\frac{46}{q}-\frac{46}{r}-\frac{46}{s}$
The given equation relates the positive variables $p$, $q$, $r$, and $s$. Which of the following is equivalent to $q$?

A

$\frac{prs}{pr+ps+rs}$

B

$\frac{prs}{46p+46r+46s}$

C

$p+r+s$

D

$46(p+r+s)$