\(B= \frac{\frac{b+c+a}{a\left ( b+c \right )}}{\frac{b+c-a}{a\left ( b+c \right )}}\times \frac{2bc+b^{2}+c^{2}-a^{2}}{2bc}\times \left ( a+b+c \right )^{-2}\)\(=\frac{b+c+a}{b+c-a}\times \frac{\left ( b+c \right )^{2}-a^{2}}{2bc}\times \left ( a+b+c \right )^{-2}\)\(=\frac{\left ( b+c+a\right )\left ( b+c+a \right )\left ( b+c-a \right )}{\left ( b+c-a \right )2bc}\times \frac{1}{(a+b+c)^2}\)\(=\frac{1}{2bc}\)Vậy $$B=\frac{1}{2bc}.$$
\(B= \frac{\frac{b+c+a}{a\left ( b+c \right )}}{\frac{b+c-a}{a\left ( b+c \right )}}\times \frac{2bc+b^{2}+c^{2}-a^{2}}{2bc}\times \left ( a+b+c \right )^{-2}\)\(=\frac{b+c+a}{b+c-a}\times \frac{\left ( b+c \right )^{2}-a^{2}}{2bc}\times \left ( a+b+c \right )^{-2}\)\(=\frac{\left ( b+c+a\right )\left ( b+c+a \right )\left ( b+c-a \right )}{\left ( b+c-a \right )2bc}\times \left ( a+b+c \right )^{-2}\)\(=\frac{1}{2bc}\)
\(B= \frac{\frac{b+c+a}{a\left ( b+c \right )}}{\frac{b+c-a}{a\left ( b+c \right )}}\times \frac{2bc+b^{2}+c^{2}-a^{2}}{2bc}\times \left ( a+b+c \right )^{-2}\)\(=\frac{b+c+a}{b+c-a}\times \frac{\left ( b+c \right )^{2}-a^{2}}{2bc}\times \left ( a+b+c \right )^{-2}\)\(=\frac{\left ( b+c+a\right )\left ( b+c+a \right )\left ( b+c-a \right )}{\left ( b+c-a \right )2bc}\times \f
rac{1}{(a+b+c)^2}\)\(=\frac{1}{2bc}\)
Vậy $$B=\frac{1}{2bc}.$$