A curve is defined by the parametric equations: X = 3 – 4t , y = 1 + (2/t) Find (dy/dx) in terms of t.

When dividing fractions by fractions with a common factor:

(a/c) / (b/c) = (a/c) * (c/b) = (ac/bc) we can cancel the common factor to get (a/b).

So in this question we can do the same:

(dy/dt) / (dx/dt) = (dy/dt) * (dt/dx) = (dy/dx)

So calculating dy/dt:

Using d/dx x^n = nx^(n-1)

Y = 1 + (2/t) = 1 + 2t^(-1)

dy/dt = 0 – 2t^(-2) = -2/t^(2)

Calculating dx/dt:

X = 3 – 4t

dy/dx = -4

Finally, dy/dx:

dy/dx = (dy/dt) / (dx/dt) = (-2/t^(2)) / (-4) = -2/(-4t^2)

= 1/2t^2