Question

If $y=\frac{2x+1}{2x-1}$, we can express x in terms of y as$x=a\left(\frac{y+1}{y-1}\right).Find\frac{1}{a}$

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Answer 1

y = $\frac{2x+1}{2x-1}$

$\Rightarrow$ 2yx - y = 2x + 1

$\Rightarrow$ (2y - 2)x = y + 1

$x=\frac{y+1}{2y-2}=\frac{1}{2}\left(\frac{y+1}{y-1}\right)$

Comparing it with $a\left(\frac{y+1}{y-1}\right)$ gives

$a=\frac{1}{2}$

$\frac{1}{a}=2$