Question

6．已知實(shí)數(shù)x、y、z滿足$\left\{\begin{array}{l}{4x-3y=0}\\{3y-2z=0}\end{array}\right.$，試求$\frac{x+2y-z}{2x-y+z}$的值．

Answer 1

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

解答 解：∵實(shí)數(shù)x、y、z滿足$\left\{\begin{array}{l}{4x-3y=0}\\{3y-2z=0}\end{array}\right.$，
∴x=$\frac{3}{4}$y，z=$\frac{3}{2}$y，
將x=$\frac{3}{4}$y，z=$\frac{3}{2}$y代入$\frac{x+2y-z}{2x-y+z}$可得：
$\frac{x+2y-z}{2x-y+z}$
=$\frac{\frac{3}{4}y+2y-\frac{3}{2}y}{2×\frac{3}{4}y-y+\frac{3}{2}y}$
=$\frac{5}{8}$．

點(diǎn)評 本題考查了分式的值，解答本題的關(guān)鍵在于根據(jù)x、y、z滿足$\left\{\begin{array}{l}{4x-3y=0}\\{3y-2z=0}\end{array}\right.$，求出：x=$\frac{3}{4}$y，z=$\frac{3}{2}$y，然后代入求值．