Question

Tìm x : 

(x-2)/(x-1) = (x+4)/(x+7)

Answer 1

x=5       

Answer 2

\(\text{Áp dụng tính chất của dãy tỉ số bằng nhau ta có:}\)

\(\frac{x-2}{x-1}=\frac{x+4}{x+7}=\frac{\left(x-2\right)-\left(x+4\right)}{\left(x-1\right)-\left(x+7\right)}=\frac{x-2-x-4}{x-1-x-7}=\frac{-6}{-8}=\frac{3}{4}\)

\(\text{Suy ra: }\frac{x-2}{x-1}=\frac{3}{4}\Rightarrow3.\left(x-1\right)=4.\left(x-2\right)\)

\(\Rightarrow3x-3=4x-8\)

\(\Rightarrow3x-4x=-8+3\)

\(\Rightarrow-x=-5\Rightarrow x=5\)