Find the value

Splitting the middle term,

$=x^{2}+\frac{5}{35} x+\frac{7}{35} x+\frac{1}{35}$

$\left[\therefore \frac{12}{35}=\frac{5}{35}+\frac{7}{35}\right.$ and $\left.\frac{5}{35} \times \frac{7}{35}=\frac{1}{35}\right]$

$=x^{2}+x / 7+x / 5+1 / 35$

$=x(x+1 / 7)+1 / 5(x+1 / 7)$

$=(x+1 / 7)(x+1 / 5)$

$\therefore \mathrm{x}^{2}+\frac{12}{35} \mathrm{x}+\frac{1}{35}=\left(\mathrm{x}+\frac{1}{7}\right)\left(\mathrm{x}+\frac{1}{5}\right)$