Giải:
\(x+1:x+5=x-1:x-3\)
\(\Leftrightarrow\dfrac{x+1}{x+5}=\dfrac{x-1}{x-3}\)
\(\Leftrightarrow\left(x+1\right).\left(x-3\right)=\left(x+5\right).\left(x-1\right)\)
\(\Leftrightarrow x^2+x-3x-3=x^2+5x-x-5\)
\(\Leftrightarrow x^2-2x-3=x^2+4x-5\)
\(\Leftrightarrow x^2-x^2-2x-4x-3=-5\)
\(\Leftrightarrow-6x-3=-5\)
\(\Leftrightarrow-6x=-5+3\)
\(\Leftrightarrow-6x=-2\)
\(\Leftrightarrow x=\dfrac{-2}{-6}=\dfrac{1}{3}\)
Vậy \(x=\dfrac{1}{3}\).
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