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? $$x-14=(x-13)-1\\x-15=(x-14)-1\\..?$$

Hint: Note that
$$\frac{x-13}{x-14} = \frac{x-14+1}{x-14} = 1 + \frac{1}{x-14} \tag{1}\label{eq1A}$$
$$\frac{x-15}{x-16} = \frac{x-16+1}{x-16} = 1 + \frac{1}{x-16} \tag{2}\label{eq2A}$$
