\(slope ~=~ \frac{dy}{dx} \)

\(\frac{dy}{dx} = \frac{(x+1) - x}{(x+1)^2}\)

\(\frac{dy}{dx} = \frac{1}{(x+1)^2}\)

\(\frac{1}{4} = \frac{1}{(x+1)^2}\)

\(\frac{1}{4}(x^2 +2x + 1 ) = 1\)

\(x^2 +2x -3 = 0\)

\(x_1 = \frac{-2+\sqrt{2^2 + 4(1)(3)}}{2(1)} \)

\(x_1 = 1\)

\(y_1 =\frac{1}{2} \)

One point is at \((1, \frac{1}{2})\)

\(x_2 = \frac{-2-\sqrt{2^2 + 4(1)(3)}}{2(1)} \)

\(x_2=-3\)

\(y_1 =\frac{-3}{-2} \)

The second point is at \((-3, \frac{3}{2})\)