Find y from Mixed Direct–Inverse Variation

If $y$ equals the sum of two quantities, one varying directly as $x$ and the other varying inversely as $x^2$, and $y=19$ when $x=2$ or $x=3$, find $y$ as a function of $x$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. III. Variation, Examples III, No. 10