Question

16．已知$\frac{x}{y+z}=a，\frac{y}{x+z}=b，\frac{z}{x+y}=c$，且abc≠0，求$\frac{a}{a+1}+\frac{b+1}+\frac{c}{c+1}$的值．

Answer 1

分析 把已知數(shù)據(jù)代入所求的代數(shù)式，根據(jù)分式的通分、約分法則計(jì)算即可．

解答 解：$\frac{a}{a+1}+\frac{b+1}+\frac{c}{c+1}$
=$\frac{\frac{x}{y+z}}{\frac{x}{y+z}+1}$+$\frac{\frac{y}{x+z}}{\frac{y}{x+z}+1}$+$\frac{\frac{z}{x+y}}{\frac{z}{x+y}+1}$
=$\frac{x}{x+y+z}$+$\frac{y}{x+y+z}$+$\frac{z}{x+y+z}$
=1．

點(diǎn)評(píng) 本題考查的是分式的化簡求值，正確運(yùn)用整體代入思想、掌握分式的約分法則是解題的關(guān)鍵．