Answer
$y = \dfrac{Cx^2}{x+1}$`
Work Step by Step
RECALL:
For positive real numbers M and N:
(1) $\ln{M} = \ln{N} \longrightarrow M=N$
(2) Product Rule: $\ln{M} + \ln{N} = \ln{(MN)}$
(3) Quotient Rule: $\ln{M} - \ln{N} = \ln{\left(\dfrac{M}{N}\right)}$
(4) Power Rule: $r\cdot ln {M} = \ln{(M^r)}$
Use rule the Power Rule to obtain:
$\ln{y}=2\ln{x}-\ln{(x+1)}+\ln{C}
\\\ln{y} = \ln{x^2}-\ln{(x+1)}+\ln{C}$
Apply the Quotient Rule to the first two terms of the right side of the equation to obtain:
$\ln{y} = \ln{\left(\dfrac{x^2}{x+1}\right)}+\ln{C}$
Apply the Product Rule to obtain:
$\ln{y} = \ln{\left[\left(\dfrac{x^2}{x+1}\right) \cdot C\right]} \\\ln{y} = \ln{\left(\dfrac{Cx^2}{x+1}\right)}$
Use rule (1) above to obtain:
$y = \dfrac{Cx^2}{x+1}$`