Question

Bài 2 : Cho x,y,z khác 0 và x - y-z = 0. Tính giá trị của biểu thức : B = \(\left(1-\dfrac{z}{x}\right).\left(1-\dfrac{x}{y}\right).\left(1+\dfrac{y}{z}\right)\)

Answer 1

x-y-z=0

\(\Rightarrow x=y+z\)

\(\Rightarrow y=x-z\)

\(\Rightarrow-z=y-z\)

\(B=\left(1-\dfrac{z}{x}\right).\left(1-\dfrac{y}{x}\right).\left(1+\dfrac{y}{z}\right)\)

\(B=\left(\dfrac{x-z}{x}\right).\left(\dfrac{y-x}{y}\right).\left(\dfrac{z+y}{z}\right)\)

\(B=(\dfrac{y}{x}).\left(\dfrac{-z}{y}\right).\left(\dfrac{x}{z}\right)\)

\(B=\dfrac{\left(y.x.-z\right)}{\left(y.x.z\right)}\Rightarrow B=-1\)

Answer 2