Answer:
B
Step-by-step explanation:
Simplify the sum on the denominator, that is
[tex]\frac{1}{x+2}[/tex] + [tex]\frac{1}{x+3}[/tex]
multiply numerator/ denominator of first fraction by x + 3
Multiply numerator/ denominator of second fraction by x+ 2
= [tex]\frac{x+3}{(x+2)(x+3)}[/tex] + [tex]\frac{x+2}{(x+2)(x+3)}[/tex]
= [tex]\frac{2x+5}{x^2+5x+6}[/tex]
The original fraction is now
[tex]\frac{1}{\frac{2x+5}{x^2+5x+6} }[/tex]
= 1 × [tex]\frac{x^2+5x+6}{2x+5}[/tex]
= [tex]\frac{x^2+5x+6}{2x+5}[/tex] → B
