# How do you derive y = -1/(1+x^2)+1/x^2 using the quotient rule?

$\frac{- 4 {x}^{3} - 2 x}{{x}^{4} {\left(1 + {x}^{2}\right)}^{2}}$
To simplify the matters, add both the fractions = $\frac{1}{{x}^{2} \left(1 + {x}^{2}\right)}$ = 1/((x^4 +x^2 )
Now use quotient rule y' = $\frac{0 \left({x}^{2} + {x}^{4}\right) - 1 \left(4 {x}^{3} + 2 x\right)}{{x}^{4} {\left(1 + {x}^{2}\right)}^{2}}$
=$\frac{- 4 {x}^{3} - 2 x}{{x}^{4} {\left(1 + {x}^{2}\right)}^{2}}$