Question 33114
{{{ ((x-5)/(x^2+2x-3))-((x-1)/(x^2+6x+9)) }}}
{{{ ( (x-5)/((x+3)(x-1)) )-( (x-1)/((x+3)(x+3)) ) }}}


Common multiple is (x+3)(x+3)(x-1), so multiply first term by 1 but written as (x+3)/(x+3). And multiply second term by 1 but written as (x-1)/(x-1).


{{{ ( (x-5)/((x+3)(x-1)) )*((x+3)/(x+3)) - ( (x-1)/((x+3)(x+3)) )*((x-1)/(x-1)) }}}
{{{ ( ((x-5)(x+3))/((x+3)(x+3)(x-1)) ) - ( ((x-1)(x-1))/((x-1)(x+3)(x+3)) ) }}}
{{{ ( ((x-5)(x+3)) - ((x-1)(x-1)) )/((x+3)(x+3)(x-1)) }}}
{{{ ( (x^2-2x-15) - (x^2-2x+1) )/((x+3)(x+3)(x-1)) }}}
{{{ ( x^2-2x-15-x^2+2x-1 )/((x+3)(x+3)(x-1)) }}}
{{{ (-16)/((x+3)(x+3)(x-1)) }}}


jon.