Let's perform the operations:

$$
\left(1-\frac{x^{2}+4 x+3}{2 x^{2}+3 x+1}\right):\left(1-\frac{x^{2}+3}{2 x^{2}-5 x-3}\right)=?
$$
Performing the indicated operations, we obtain:

$$
\frac{x^{2}-5 x+6}{x^{2}-5 x-6}
$$

The problem was solved by: Ehrenstein P., Füstös P., Makó E., Paunz A., Schwarz Gy., Steiger J., Szabó J., Tóth B. of the Budapest branch of the h. y. dental school V. class.