Instead of using the quotient rule, you can first expand y :
y = (4x - 1)^2 / x ^2 = (16x ^2 - 8x + 1) / x ^2 = 16 - 8/x + 1/x ^2
Then the derivative is
dy/dx = -8/x ^2 - 2/x ^3
The tangent to the curve at (-1, 25) then has a slope or gradient of
dy/dx = -8/(-1)^2 - 2/(-1)^3 = -6
