Question

15．已知x，y，z均不为零，且有4x-3y-3z=x-3y+z=0，求$\frac{y}{z}-\frac{x}{z}$的值．

Answer 1

分析 根据4x-3y-3z=x-3y+z=0，转化为方程组$\left\{\begin{array}{l}{4x-3y-3z=0}\\{x-3y+z=0}\end{array}\right.$，解得：$\left\{\begin{array}{l}{x=\frac{4}{3}z}\\{y=\frac{7}{9}z}\end{array}\right.$，代入即可解答．

解答 解：∵4x-3y-3z=x-3y+z=0，
∴$\left\{\begin{array}{l}{4x-3y-3z=0}\\{x-3y+z=0}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{x=\frac{4}{3}z}\\{y=\frac{7}{9}z}\end{array}\right.$，
∴$\frac{y}{z}-\frac{x}{z}=\frac{\frac{7}{9}z}{z}-\frac{\frac{4}{3}z}{z}=\frac{7}{9}-\frac{4}{3}=-\frac{5}{9}$．

点评 本题考查了分式的化简求值，解决本题的关键是把4x-3y-3z=x-3y+z=0，转化为方程组$\left\{\begin{array}{l}{4x-3y-3z=0}\\{x-3y+z=0}\end{array}\right.$．