Answer
$\dfrac{x+1}{x+4}$
Work Step by Step
Factoring the expressions and then cancelling the common factors between the numerator and the denominator, the given expression, $
\dfrac{x^2+x-2}{x^2+5x+6}\div\dfrac{x^2+3x-4}{x^2+4x+3}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^2+x-2}{x^2+5x+6}\cdot\dfrac{x^2+4x+3}{x^2+3x-4}
\\\\=
\dfrac{(x+2)(x-1)}{(x+2)(x+3)}\cdot\dfrac{(x+3)(x+1)}{(x+4)(x-1)}
\\\\=
\dfrac{(\cancel{x+2})(\cancel{x-1})}{(\cancel{x+2})(\cancel{x+3})}\cdot\dfrac{(\cancel{x+3})(x+1)}{(x+4)(\cancel{x-1})}
\\\\=
\dfrac{x+1}{x+4}
.\end{array}
