All fractions which can be written simultaneously in the forms $\frac{7k-5}{5k-3}$ and $\frac{6l-1}{4l-3}$ Find all fractions which can be written simultaneously in the forms $\frac{7k-5}{5k-3}$ and $\frac{6l-1}{4l-3}$
for some integers $k,l$.

Please check my answer and tell me is correct or not....
$$\frac{43}{31},\frac{31}{27},1,\frac{55}{39},\frac{5}{3},\frac{61}{43},\frac{19}{13},\frac{13}{9}$$


Suppose there is integer $p$ which can be written as $\frac{6l-1}{4l-3}$ and $\frac{7k-5}{5k-3}$. 
$$p= \frac{6l-1}{4l-3} =\frac{7k-5}{5k-3}$$
$$\implies kl+8k+l=6$$
$$\implies(k+1)l=(6-8k)\implies l=\frac{-2(4k-3)}{(k+1)}$$.
Which gives following integer solutions:
$(k,l)=(-15,-9),(-8,-10),(-3,-15),(-2,-22),(0,6),(1,-1),(6,-6),(13,7)$. These all sets of values will give you a new such number. I shall let you conclude now.
