Lore For Math

${\displaystyle \underset{‾}{\frac{1}{x^2(ax+b)}=\frac{1}{b{x}^2}-\frac{a}{b^{2}x}+\frac{a}{b}\cdot \frac{1}{ax+b}\mathrm{.}}}$

${\displaystyle \frac{1}{x^2(ax+b)}}$

${\displaystyle =\frac{1}{x}\frac{1}{x(ax+b)}}$

${\displaystyle cite\frac{1}{x(ax+b)}=\frac{1}{b}(\frac{1}{x}-\frac{a}{ax+b}),}$

${\displaystyle =\frac{1}{bx}(\frac{1}{x}-\frac{a}{ax+b})}$

${\displaystyle =\frac{1}{b}(\frac{1}{x^2}-a\frac{1}{x(ax+b)})}$

${\displaystyle cite\frac{1}{x(ax+b)}=\frac{1}{b}(\frac{1}{x}-\frac{a}{ax+b}),}$

${\displaystyle =\frac{1}{b}\left(\frac{1}{x^2}-\frac{a}{b}(\frac{1}{x}-\frac{a}{ax+b})\right)}$

${\displaystyle =\frac{1}{b{x}^2}-\frac{a}{b^{2}x}+\frac{a}{b}\cdot \frac{1}{ax+b}\mathrm{.}}$