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Given the equation y = (pi − x) / x, express x in terms of y.

April 18, 2026Mathematics

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Answer

x = \frac{\pi}{y+1}

Graph of y = (π − x)/x

Key points of y = (π − x)/x
Point	x	y
x-intercept	3.14	0

4 steps

here is the solution for the equation:

y = \frac{\pi - x}{x}

The goal is to express $x$ in terms of $y$ .

Multiply both sides of the equation by $x$ to eliminate the denominator.
$yx = \pi - x$
Add $x$ to both sides of the equation to gather all terms containing $x$ on one side.
$yx + x = \pi$
Factor out $x$ from the terms on the left side.
$x(y + 1) = \pi$
Divide both sides by $(y+1)$ to isolate $x$ .
$x = \frac{\pi}{y+1}$
The solution for $x$ in terms of $y$ is:
$\boxed{x = \frac{\pi}{y+1}}$
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