Maximum value of a fraction

Find the greatest value of $\frac{x + 2}{2 x ^{2} + 3 x + 6}$ for real values of $x$ .

~10 minAnswer checked instantlyExtremaDiscriminant method

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.b, No. 11

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).