Question

6．已知实数x、y、z满足$\left\{\begin{array}{l}{4x-3y=0}\\{3y-2z=0}\end{array}\right.$，试求$\frac{x+2y-z}{2x-y+z}$的值．

Answer 1

分析 先根据x、y、z满足$\left\{\begin{array}{l}{4x-3y=0}\\{3y-2z=0}\end{array}\right.$，求出：x=$\frac{3}{4}$y，z=$\frac{3}{2}$y，然后代入求值即可．

解答 解：∵实数x、y、z满足$\left\{\begin{array}{l}{4x-3y=0}\\{3y-2z=0}\end{array}\right.$，
∴x=$\frac{3}{4}$y，z=$\frac{3}{2}$y，
将x=$\frac{3}{4}$y，z=$\frac{3}{2}$y代入$\frac{x+2y-z}{2x-y+z}$可得：
$\frac{x+2y-z}{2x-y+z}$
=$\frac{\frac{3}{4}y+2y-\frac{3}{2}y}{2×\frac{3}{4}y-y+\frac{3}{2}y}$
=$\frac{5}{8}$．

点评 本题考查了分式的值，解答本题的关键在于根据x、y、z满足$\left\{\begin{array}{l}{4x-3y=0}\\{3y-2z=0}\end{array}\right.$，求出：x=$\frac{3}{4}$y，z=$\frac{3}{2}$y，然后代入求值．