2.3 Product and quotient rules; question 25

[Eigenvalue]

Find the derivative of the algebraic function
f(x)=[tex]\frac{3-2x-x²}{x²-1}[/tex]

[Eigenvalue]

The quotient rule: f'(x)=[tex]\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))²}[/tex]

f'(x)=[tex]\frac{(-2x-2)(x²-1)-2x(3-2x-x²)}{(x²-1)²}[/tex]
=[tex]\frac{-2x³-2x²+2x+2+2x³+4x²-6x}{x⁴-2x²+1}[/tex]
=[tex]\frac{2x²-4x-2}{x⁴-2x²+1}[/tex]