Question 1019520
{{{ (6/n^2) - (1/n) = -( 1/(3n) ) }}}
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Just multiply both sides by {{{ 3n^2 }}}
I'll do it step by step:
{{{ 3n^2*( 6/n^2 ) - 3n^2*( 1/n ) = 3n^2*( -1/(3n) ) }}}
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I'll rearrange
{{{ ( n^2/n^2 )*18 - ( n^2/n )*3 = ( n^2/n )*(-1) }}}
{{{ 18 - 3n = (-1)*n }}}
{{{ 18 - 3n + n = 0 }}}
{{{ 18 - 2n = 0 }}}
{{{ 2n = 18 }}}
{{{ n = 9 }}}
Check:
{{{ (6/n^2) - (1/n) = -( 1/(3n) ) }}}
{{{ (6/9^2) - (1/9) = -( 1/(3*9) ) }}} 
{{{ 6/81 - 9/81  = -1/27 }}}
{{{ 6/81 - 9/81 = -3/81 }}}
{{{ -3/81 = -3/81 }}}
OK