Answer
$\dfrac {x+1}{x+4}$
Work Step by Step
$\dfrac {x^{2}+x-2}{x^{2}+5x+6}:\dfrac {x^{2}+3x-4}{x^{2}+4x+3}=\dfrac {\left( x+2\right) \left( x-1\right) }{\left( x+2\right) \left( x+3\right) }:\dfrac {\left( x+4\right) \left( x-1\right) }{\left( x+3\right) \left( x+1\right) }=\dfrac {\left( x+2\right) \left( x-1\right) }{\left( x+2\right) \left( x+3\right) }\times \dfrac {\left( x+3\right) \left( x+1\right) }{\left( x+4\right) \left( x-1\right) }=\dfrac {x+1}{x+4}$
