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If x=(1-t^2)/(1+t^2) and y=(2t)/(1+t^2),...

If `x=(1-t^2)/(1+t^2)` and `y=(2t)/(1+t^2)`, prove that `dy/dx+x/y=0`

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To prove that \(\frac{dy}{dx} + \frac{x}{y} = 0\) given \(x = \frac{1 - t^2}{1 + t^2}\) and \(y = \frac{2t}{1 + t^2}\), we will follow these steps: ### Step 1: Find \(\frac{dy}{dt}\) Using the quotient rule, we differentiate \(y\) with respect to \(t\): \[ y = \frac{2t}{1 + t^2} \] Let \(u = 2t\) and \(v = 1 + t^2\). Then, ...
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