Solve the following

$\frac{3 x+5}{4 x+2}=\frac{3 x+4}{4 x+7}$

$\Rightarrow(4 x+7)(3 x+5)=(4 x+2)(3 x+4) \quad$ (by cross multiplication)

$\Rightarrow 12 x^{2}+20 x+21 x+35=12 x^{2}+16 x+6 x+8$

$\Rightarrow 12 x^{2}+41 x+35=12 x^{2}+22 x+8$

$\Rightarrow 12 x^{2}-12 x^{2}+41 x-22 x=8-35$

$\Rightarrow 19 x=-27$

$\Rightarrow x=\frac{-27}{19}$

$\therefore x=\frac{-27}{19}$