<s>[INST] Solve the equation $\frac{x-13}{x-14}-\frac{x-15}{x-16}=-\frac{1}{12}$ Solve the equation $$\dfrac{x-13}{x-14}-\dfrac{x-15}{x-16}=-\dfrac{1}{12}.$$
For $x\ne14$ and $x\ne 16$ by multiplying the whole equation by $$12(x-14)(x-16)$$ we get: $$12(x-16)(x-13)-12(x-14)(x-15)=-(x-14)(x-16).$$ This doesn't look very nice. Can we do something else at the beginning? $$x-14=(x-13)-1\\x-15=(x-14)-1\\..?$$
 [/INST] Hint: Notice that if we visually erase the symbols "$x - 1$" in both numerators and denominators we are left with $\frac34$ and $\frac56$ respectively, which is nice because
$$
\frac34 = \frac{9}{12}\quad\text{and}\quad\frac56 = \frac{10}{12}.
$$
</s>