Simplifying

Algebra Level 3

Simplify x + 1 x 3 − x \dfrac{x+1}{x^3-x} as much as you can.

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Note: x 3 ≠ 1 x^3 \neq 1

1 x 3 − 1 x \dfrac{1}{x^3}-\dfrac{1}{x} 1 x 2 − 1 \dfrac{1}{x^2-1} 1 x 2 + x \dfrac{1}{x^2+x} 1 x 3 \dfrac{1}{x^3} 1 x 2 − x \dfrac{1}{x^2-x} 1 x 2 − 1 x 3 \dfrac{1}{x^2}-\dfrac{1}{x^3}

Terry Yu by Terry Yu , 17, USA

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1 solution

Terry Yu
May 16, 2017

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

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