According to Kohlrausch's law of independent migration of ions, the limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of its anion and cation.

$\Lambda^{\circ}_m(\text{CH}_3\text{COOH}) = \lambda^{\circ}_m(\text{CH}_3\text{COO}^-) + \lambda^{\circ}_m(\text{H}^+)$

We can obtain this by adding the molar conductivities of $\text{CH}_3\text{COONa}$ and $\text{HCl}$, and subtracting the molar conductivity of $\text{NaCl}$:

$\Lambda^{\circ}_m(\text{CH}_3\text{COOH}) = \Lambda^{\circ}_m(\text{CH}_3\text{COONa}) + \Lambda^{\circ}_m(\text{HCl}) - \Lambda^{\circ}_m(\text{NaCl})$

Substituting the given values: $\Lambda^{\circ}_m(\text{CH}_3\text{COOH}) = 91.0 + 426.16 - 126.45$ $\Lambda^{\circ}_m(\text{CH}_3\text{COOH}) = 517.16 - 126.45 = 390.71 \text{ S cm}^2\text{ mol}^{-1}$