Learn how to solve problems step by step online. Find the derivative d/dx(((x-2)(x+4))/((x-1)(x+3))). Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The power of a product is equal to the product of it's factors raised to the same power. Simplify the product -(x-2). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x-2 and g=x+4.

Find the derivative d/dx(((x-2)(x+4))/((x-1)(x+3)))