Question

Tìm x biết : \(\frac{x-1}{x+2}=\frac{x-2}{x+3}\)

 

Answer 1

\(\frac{x-1}{x+2}=\frac{x-2}{x+3}\)

\(\Rightarrow\left(x-1\right)\left(x+3\right)=\left(x-2\right)\left(x+2\right)\)

\(\Rightarrow x^2+2x-3=x^2-4\)

\(\Rightarrow x^2+2x-x^2=-4+3\) ( qui tắc chuyển vế )

\(\Rightarrow2x=-1\)

\(\Rightarrow x=-\frac{1}{2}\)

 

Answer 2

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)=\left(x-1\right)\left(x+3\right)\)

\(\Leftrightarrow x^2-4=x^2+2x-3\)

\(\Leftrightarrow x^2-x^2-2x=-3+4\)

\(\Leftrightarrow-2x=1\)

\(\Leftrightarrow x=\frac{-1}{2}\)