Prove that if limxa[f(x)+g(x)]=M and limxaf(x)=L then limxag(x) exists and is equal to ML.

Problem: 

Prove that if
limxa[f(x)+g(x)]=M and limxaf(x)=L
then
limxag(x)
exists and is equal to ML.

Answer: 

limxag(x)=ML