Question 542285
{{{ (3/(x-3))=(-3/(x+6))+(3/((x-3)(x+6))) }}}
Divide both sides by {{{3}}}
{{{ (1/(x-3))=(-1/(x+6))+(1/((x-3)(x+6))) }}}
Multiply both sides by {{{ (x-3 )*( x + 6 ) }}}
{{{ x + 6 = -( x - 3 ) + 1 }}}
{{{ x + 6 = -x + 3 + 1 }}}
{{{ 2x = 4 - 6 }}}
{{{ 2x = -2 }}}
{{{ x = -1 }}}
check answer:
{{{ (3/(x-3))=(-3/(x+6))+(3/((x-3)(x+6))) }}}
{{{ (3/(-1-3))=(-3/(-1+6))+(3/((-1-3)(-1+6))) }}}
{{{ (3/(-4))=(-3/(5))+(3/((-4)*5)) }}}
{{{ -3/4 = -3/5 -3/20 }}}
{{{ -1/4 = -1/5 -1/20 }}}
Multiply both sides by {{{20}}}
{{{ -5 = -4 - 1 }}}
{{{ -5 = -5 }}}
OK