The numerator of the given expression can be rewritten in terms of the denominator, x – 3, as follows: x2−2x−5=x2−3x+x−3−2, which is equivalent to x(x–3)+(x–3)–2. So t he given expression is equivalent to
x(x−3)+(x−3)−2
x−3
=
x(x−3)
x−3
+
x−3
x−3
−
2
x−3
Since the given expression is defined for x ≠ 3, the expression can be rewritten as x+1−
2
x−3
. Long division can also be used as an alternate approach.