Question

Cho biết \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\) . Tính gt của bt M = \(\dfrac{y+z-x}{x-y+z}\)

giúp mk nha các bạn siêu toán

Answer 1

Đặt \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=k\) \(\left(k\ne0\right)\)

\(\Rightarrow\left\{{}\begin{matrix}x=2k\\y=3k\\z=4k\end{matrix}\right.\)

\(\Rightarrow M=\dfrac{y+z-x}{x-y+z}=\dfrac{3k+4k-2k}{2k-3k+4k}=\dfrac{\left(3+4-2\right)\times k}{\left(2-3+4\right)\times k}=\dfrac{5k}{3k}=\dfrac{5}{3}\)

Vậy \(M=\dfrac{5}{3}\).

Answer 2

Làm đúng cách lớp 7:

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{y+z-x}{3+4-2}=\dfrac{y+z-x}{5}=\dfrac{x-y+z}{2-3+4}=\dfrac{x-y+z}{3}\)

\(\Rightarrow M=\dfrac{x+z-x}{x-y+z}=\dfrac{5}{3}\)