Differentiate

y = (x + 1)(x - 5) / (2x - 3)

Differentiate both sides with respect to x

dy/dx

= [(2x - 3)d/dx (x + 1)(x - 5) - (x + 1)(x - 5) d/dx (2x - 3)] / (2x - 3)^2

= [(2x - 3)[(x - 5) + (x + 1)] - (x + 1)(x - 5)(2)] / (2x - 3)^2

= [(2x - 3)(2x - 4) - 2(x + 1)(x - 5)] / (2x - 3)^2

= [4x^2 - 14x + 12 - 2x^2 + 8x + 10] / (2x - 3)^2

= (2x^2 - 6x + 22) / (2x - 3)^2

= 2(x^2 - 3x + 11) / (2x - 3)^2