Factorize the following expression : \(x^2 + \frac{12}{35}x + \frac{1}{35}\)
\[
x^2 + \frac{12}{35}x + \frac{1}{35}
\]
\[
= x^2 + \frac{5}{35}x + \frac{7}{35}x + \frac{1}{35}
\]
\[
= x\left(x + \frac{1}{7}\right) + \frac{1}{5}\left(x + \frac{1}{7}\right)
\]
\[
= \left(x + \frac{1}{7}\right)\left(x + \frac{1}{5}\right)
\]