In: Math

Find equations of the tangent lines to the curve y = (x-1)/(x+1) that are parallel to the line x − 2y = 5.

Given: \(y=\frac{x-1}{x+1}\)

\(\frac{d y}{d x}=\frac{x+1-(x-1)}{(x+1)^{2}}=\frac{2}{(x+1)^{2}}\)

So, \(\frac{2}{(x+1)^{2}}=\frac{1}{2}\)

or \(x^{2}+2 x-3=0\)

\((x-1)(x+3)=0\)

\(x=1,-3\)

For \(x=1, y=0\)

For \(x=-3, y=2\)

So, equation of tan gents:

\((y-0)=\frac{1}{2}(x-1)\)

\(\& \quad(y-2)=\frac{1}{2}(x+3)\)

\(x-2 y-1=0\)

\(\& \quad x-2 y+7=0\)

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