Question

can anyone answer this sum please its urgent with correct method ​

Answer 1

$\frac{x}{1 + \frac{1}{1 + \frac{x}{1 - x} } } = 1 \\ \\ \frac{x}{1 + \frac{1}{ \frac{1(1 - x) + x}{1 - x} } } = 1 \\ \\ \frac{x}{1 + \frac{1(1 - x)}{1 - x + x} } = 1 \\ \\ \frac{x}{1 + \frac{1 - x}{1} } = 1 \\ \\ \frac{x}{ \frac{1 \times 1 + 1 - x}{1} } = 1 \\ \\ \frac{x \times 1}{1 + 1 - x} = 1 \\ \\ \frac{x}{2 - x} = 1 \\ \\ x = 1 \times (2 - x) \\ \\ x = 2 - x \\ \\ x + x = 2 \\ \\ 2x = 2 \\ \\ x = \frac{2}{2} \\ \\ x = 1.$

Answer 2

$\begin{gathered} \frac{x}{1 + \frac{1}{1 + \frac{x}{1 - x} } } = 1 \\ \\ \frac{x}{1 + \frac{1}{ \frac{1(1 - x) + x}{1 - x} } } = 1 \\ \\ \frac{x}{1 + \frac{1(1 - x)}{1 - x + x} } = 1 \\ \\ \frac{x}{1 + \frac{1 - x}{1} } = 1 \\ \\ \frac{x}{ \frac{1 \times 1 + 1 - x}{1} } = 1 \\ \\ \frac{x \times 1}{1 + 1 - x} = 1 \\ \\ \frac{x}{2 - x} = 1 \\ \\ x = 1 \times (2 - x) \\ \\ x = 2 - x \\ \\ x + x = 2 \\ \\ 2x = 2 \\ \\ x = \frac{2}{2} \\ \\ x = 1.\end{gathered}$