Question 1041844
{{{(4x+3)/(x-6)+(x-4)/(6-x)=44/(2x-12)}}}
{{{(4x+3)/(x-6)+(-x+4)/(x-6)=44/(2x-12)}}}
{{{ ( 4x + 3 - x + 4 ) / ( x - 6 ) = 44/( 2x - 12 ) }}}
{{{ ( 3x + 7 ) / ( x - 6 )  = 22 / ( x - 6 ) }}}
Note that {{{ x }}} cannot  = {{{ 6 }}}
( division by zero is not allowed )
Multiply both sides by {{{ x - 6 }}}
{{{ 3x + 7 = 22 }}}
{{{ 3x = 15 }}}
{{{ x = 5 }}}
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check:
{{{(4x+3)/(x-6)+(x-4)/(6-x)=44/(2x-12)}}}
{{{(4*5+3)/(5-6)+(5-4)/(6-5)=44/(2*5-12)}}}
{{{ 23 / (-1) + 1 / 1 = 44 / (-2) }}}
{{{ -23 + 1 = -22 }}}
{{{ -22 = -22 }}}
OK