6. A curve has parametric equations
$$x = \frac { t } { 2 - t } , \quad y = \frac { 1 } { 1 + t } , \quad - 1 < t < 2$$
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 1 } { 2 } \left( \frac { 2 - t } { 1 + t } \right) ^ { 2 }\).
- Find an equation for the normal to the curve at the point where \(t = 1\).
- Show that the cartesian equation of the curve can be written in the form
$$y = \frac { 1 + x } { 1 + 3 x }$$