When the numerator of a fraction is increased by $4$, the fraction increases by $2/3$... When the numerator of a fraction is increased by $4$, the fraction increases by $2/3$. What is the denominator of the fraction?
I tried,
Let the numerator of the fraction be $x$ and the denominator be $y$.
Accordingly, $$\frac{x+4}y=\frac xy+\frac 23$$
I am not able to find the second equation. 

We have $\frac{x+4}y={\frac xy}+{\frac 23}=\frac{3x+2y}{3y}$ but: $$\frac{x+4}{y}=\frac{\color{red}3(x+4)}{\color{red}3y}=\frac{3x+12}{3y}$$ So $$\frac{3x+12}{3y}=\frac{3x+2y}{3y}$$ So if $y\neq 0$ then $3x+12=3x+2y$.
