Solve the following equation and verify your answer:

$\frac{x+2}{x+5}=\frac{x}{x+6}$

or $\mathrm{x}^{2}+2 \mathrm{x}+6 \mathrm{x}+12=\mathrm{x}^{2}+5 \mathrm{x}$ [After $c$ ross multiplication]

or $\mathrm{x}^{2}-\mathrm{x}^{2}+8 \mathrm{x}-5 \mathrm{x}=-12$

or $3 \mathrm{x}=-12$

or $\mathrm{x}=\frac{-12}{3}$

or $\mathrm{x}=-4$

Thus, $x=-4$ is the solution of given equation. Check :

Substituting $\mathrm{x}=-4$ in the given equation, we get :

L. H. S. $=\frac{-4+2}{-4+5}=-2$

R.H.S. $=\frac{-4}{-4+6}=-2$

$\therefore$ L.H.S. $=$ R.H.S. for $x=-4$.