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a) Ta có: \(\frac{1}{{3 \times 4}} + \frac{1}{{4 \times 5}} + \frac{1}{{5 \times 6}} + \ldots + \frac{1}{{14 \times 15}} = \frac{1}{3} - \frac{1}{{15}} = \frac{4}{{15}}\)

Vậy: \(\frac{4}{{15}} = \frac{x}{{30}} \to \frac{8}{{30}} = \frac{x}{{30}} \to x = 8.\)

b) Ta có: \(\frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \ldots + \frac{1}{{90}} = \frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} + \frac{1}{{4 \times 5}} + \ldots + \frac{1}{{9 \times 10}} = \frac{1}{2} - \frac{1}{{10}} = \frac{2}{5}\)

Suy ra: \(\frac{2}{5} = \frac{6}{x} \to \frac{6}{{15}} = \frac{6}{x} \Rightarrow x = 15\)

Vậy \(x = 15\).