Method I:\(\frac{x}{x+y} = 6\)

Reciprocal both sides

\(\frac{x+y}{x} = \frac{1}{6}\)

\(1 + \frac{y}{x} = \frac{1}{6}\)

\(\frac{y}{x} = \frac{-5}{6}\)

Apply componendo / dividendo

\(\frac{y}{x+y} = \frac{-5}{6-5}\)

\(\frac{y}{x+y} = -5\)Method II\(\frac{x}{x+y} = 6\)

\(x+y = \frac{x}{6}\).............. (1)

\(y = \frac{x}{6} - x\)

\(y = \frac{-5x}{6}\) ............ (2)

Dividing (2) by (1)

\(\frac{y}{x+y} = \frac{-5x}{6} * \frac{6}{x}\)

\(\frac{y}{x+y} = -5\)
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