What is factor-x(x^2+1)^{-2}(2x)+(x^2+1)^{-1} ?

The solution to factor-x(x^2+1)^{-2}(2x)+(x^2+1)^{-1} is -((x+1)(x-1))/((x^2+1)^2)

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factor-x(x^2+1)^{-2}(2x)+(x^2+1)^{-1}

factor

- x (x^{2} + 1)^{- 2} (2 x) + (x^{2} + 1)^{- 1}

- \frac{( x + 1 ) ( x - 1 )}{( x ^{2} + 1 ) ^{2}}

Solution steps

- x (x^{2} + 1)^{- 2} (2 x) + (x^{2} + 1)^{- 1}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

(x^{2} + 1)^{- 1} = (x^{2} + 1)^{- 2} (x^{2} + 1)

= - x (x^{2} + 1)^{- 2} \cdot 2 x + (x^{2} + 1)^{- 2} (x^{2} + 1)

Factor out common term

(x^{2} + 1)^{- 2}

= (x^{2} + 1)^{- 2} (- x \cdot 2 x + x^{2} + 1)

Factor

x^{2} - 2 xx + 1 : - (x + 1) (x - 1)

= (x^{2} + 1)^{- 2} (- (x + 1) (x - 1))

Refine

= - \frac{( x + 1 ) ( x - 1 )}{( x ^{2} + 1 ) ^{2}}

∣ x - 1 ∣ = ∣ 3 x + 6 ∣

2 x^{2} - 7 x - 9

4 x - 2 \geq - 18 and 4 x + 6 \leq 30

- 144 x^{2} + 196

6 (\frac{1}{2})^{2}

What is factor-x(x^2+1)^{-2}(2x)+(x^2+1)^{-1} ?
The solution to factor-x(x^2+1)^{-2}(2x)+(x^2+1)^{-1} is -((x+1)(x-1))/((x^2+1)^2)