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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