$(a - b)^3 + (12a - b)^3 = (9a - b)^3 + (10a - b)^3$

$\Leftrightarrow (12a - b)^3 - (10a - b)^3 = (9a - b)^3 - (a - b)^3$

`<=>[(12a-b)-(10a-b)][12a-b)^2+(12a-b)(10a-b)+(10a-b)^2]=[(9a-b)-(a-b)][(9a-b)^2+(9a-b)(a-b)+(a-b)^2]`

$\begin{aligned} &\Leftrightarrow 2a\left[(12a - b)^2 + (12a - b)(10a - b) + (10a - b)^2\right] \\ &= 8a\left[(9a - b)^2 + (9a - b)(a - b) + (a - b)^2\right] \end{aligned}$

Vì $a \neq 0$ `=>`  chia 2 vế cho `2a`

$\Leftrightarrow (12a - b)^2 + (12a - b)(10a - b) + (10a - b)^2 = 4\left[(9a - b)^2 + (9a - b)(a - b) + (a - b)^2\right]$

`<=>`$364a^2 - 66ab + 3b^2 = 364a^2 - 120ab + 12b^2$

$\Leftrightarrow 364a^2 - 364a^2 - 66ab + 120ab = 12b^2 - 3b^2$

$\Leftrightarrow 54ab = 9b^2$

Vì $b \neq 0$ `=>` chia 2 vế cho `9b`

$\Leftrightarrow 6a = b$

$\Leftrightarrow \frac{a}{b} = \frac{1}{6}$

Vậy $\frac{a}{b} = \frac{1}{6}$