Answer:
The detailed simplification is shown below:
Step-by-step explanation:
Given,
[tex]\frac{x^{2}+x-6 }{x^{2} +8x+15}[/tex]
= [tex]\frac{x^{2}+3x-2x-6 }{x^{2} +5x+3x+15}[/tex]
= [tex]\frac{x(x+3) - 2(x+3)}{x(x+5) +3(x+5)}[/tex] .............simplify to get (x+3) and (x+5) as a common term.
= [tex]\frac{(x+3) (x-2)}{(x+5) (x+3)}[/tex]........... take common on numerator and denominator.
= [tex]\frac{(x-2)}{(x+5)}[/tex] ...................cancel out the common term (x+3).
Hence,
[tex]\frac{x^{2}+x-6 }{x^{2} +8x+15}[/tex] = [tex]\frac{(x-2)}{(x+5)}[/tex]
