Calculus Derivative Help PLEASE ANSWER?

Question

What is the derivative of (x^2-3x-4)/(x-2)? Thanks.

Answer 1

The function  (x² - 3x - 4)/(x - 2)

Differentiating with respect to x.

Apply quotient rule in derivatives d/dx(u/v) = (vu' - uv')/v²

Apply the formulae d/dx(xⁿ) = nx^n-1

d/dx(constant) = 0

In this case u = x² - 3x - 4, v = x - 2

u' = 2x - 3, v' = 1

Now the derivative is [(x - 2)(2x - 3) - (x² - 3x - 4)(1)]/(x - 2)²

= (2x² - 3x - 4x + 6 - x² + 3x + 4)/(x - 2)²

= (x² - 4x + 10)/(x - 2)².