Prove that $\displaystyle a=b \cos{C}+c \cos{B}$

I have that

$\displaystyle \cos{C}=\frac{x}{b} \implies x=b \cos{C}$

$\displaystyle \cos{B}=\frac{a+x}{c} \implies x=c \cos{B}-a$

Hence,

$\displaystyle a=c \cos{B}-b\cos{C}$

A difference instead of a sum??