| If \[\frac{2x}{2+\frac{1}{1+\frac{x}{1-x}}}=1,\] then value of x is |
A) 1
B) 2
C) 3
D) 4
Correct Answer: A
Solution :
| \[\frac{2x}{2+\frac{1}{1+\frac{x}{1-x}}}=1\]\[\Rightarrow \]\[\frac{2x}{2+\left( \frac{1-x}{1-x+x} \right)}=1\] |
| \[\Rightarrow \] \[\frac{2x}{2+\frac{1-x}{1}}=1\]\[\Rightarrow \]\[\frac{2x}{3-x}=1\] |
| \[\Rightarrow \] \[2x=3-x\]\[\Rightarrow \]\[3x=3\]\[\Rightarrow \]\[x=\,\,1\] |
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