Câu hỏi về tính giá trị biểu thức của phân số

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thaonguyenkmhd

Ta có $\dfrac{2a+b+c+d}{a}=\dfrac{a+2b+c+d}{b}=\dfrac{a+b+2c+d}{c}=\dfrac{a+b+c+2d}{d} \\ \rightarrow \dfrac{2a+b+c+d}{a}-1=\dfrac{a+2b+c+d}{b}-1=\dfrac{a+b+2c+d}{c}-1=\dfrac{a+b+c+2d}{d}-1 \\ \rightarrow \dfrac{a+b+c+d}{a}=\dfrac{a+b+c+d}{b}=\dfrac{a+b+c+d}{c}=\dfrac{a+b+c+d}{d}$

+ Nếu $a+b+c+d \ \not= \ 0 \rightarrow a=b=c=d \rightarrow M=1+1+1+1=4$

+ Nếu $a+b+c+d=0 \\ \rightarrow a+b=-(c+d) \\ b+c=-(d+a) \\ c+d=-(a+b) \\ d+a=-(b+c) \\ \rightarrow M=-1-1-1-1=-4$
 
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