#### Answer

$\dfrac{x+1}{2x^{2}+5x+3}\div\dfrac{20x+100}{2x+3}=\dfrac{1}{20(x+5)}$

#### Work Step by Step

$\dfrac{x+1}{2x^{2}+5x+3}\div\dfrac{20x+100}{2x+3}$
Factor the denominator of the first fraction and take out common factor $20$ from the numerator of the second fraction:
$\dfrac{x+1}{2x^{2}+5x+3}\div\dfrac{20x+100}{2x+3}=\dfrac{x+1}{(2x+3)(x+1)}\div\dfrac{20(x+5)}{2x+3}$
Evaluate the division of the two rational expressions and simplify by removing repeated factors in the numerator and the denominator:
$...=\dfrac{(2x+3)(x+1)}{20(2x+3)(x+1)(x+5)}=\dfrac{1}{20(x+5)}$