<PRE><B>Question 31609</B>
{{{ (16/(x^2+2x-3))-(4/(x+3)) }}}
Factor the Denom of the first fraction
{{{ (16/(x+3)(x-1))-(4/(x+3)) }}}
Multiply the second fraction by {{{ (x-1)/(x-1) }}} to get a common denom.
{{{ (16/(x+3)(x-1))-(4/(x+3))((x-1)/(x-1)) }}}
Multiply the numerator of the second fraction
{{{ (16/(x+3)(x-1))-(4(x-1)/(x+3)(x-1)) }}}
{{{ (16/(x+3)(x-1))-((4x-4)/(x+3)(x-1))) }}}
Now that you have like denominators, subtract the numerators (WATCH YOUR SIGNS)
{{{ ((16-4x+4)/(x+3)(x-1)) }}}
Combine like terms on top
{{{ ((20-4x)/(x+3)(x-1)) }}} You can Factor out a -4 on the top as well.  Some instructors will want you to leave it alone at this point.
{{{ (-4(x-5))/(x+3)(x-1) }}}

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