Question

tìm x

a/\(\dfrac{7}{x+1}=\dfrac{x+1}{9}\)

b/\(\dfrac{x-1}{x+2}=\dfrac{x-2}{x+3}\)

Answer 1

a) \(\dfrac{7}{x+1}=\dfrac{x+1}{9}\) \(\Leftrightarrow\) \(\left(x+1\right)^2=63\Leftrightarrow\left\{{}\begin{matrix}x+1=\sqrt{63}\\x+1=-\sqrt{63}\end{matrix}\right.\)

\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=\sqrt{63}-1\\x=-\sqrt{63}-1\end{matrix}\right.\) vậy \(x=-\sqrt{63}-1;x=\sqrt{63}-1\)

b) \(\dfrac{x-1}{x+2}=\dfrac{x-2}{x+3}\) \(\Leftrightarrow\) \(x^2-4=x^2+3x-x-3\)

\(\Leftrightarrow\) \(x^2-4=x^2+2x-3\) \(\Leftrightarrow\) \(x^2-4-x^2-2x+3=0\)

\(\Leftrightarrow\) \(-2x-1=0\) \(\Leftrightarrow\) \(-2x=1\Leftrightarrow x=\dfrac{-1}{2}\) vậy \(x=\dfrac{-1}{2}\)