Simplify it.

Algebra Level 2

x + 1 x 3 − x \frac{x+1}{x^3-x} is equivalent to:
Q) 1 x 2 \frac{1}{x^2} - 1 x 3 \frac{1}{x^3}
W) 1 x 3 \frac{1}{x^3} - 1 x \frac{1}{x}
E) 1 x 2 − 1 \frac{1}{x^2-1}
R) 1 x 2 − x \frac{1}{x^2-x}
T) 1 x 3 \frac{1}{x^3}

Q T E R W None of the given choices

Kenny O. by Kenny O. , 17, Singapore

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1 solution

Kenny O.
Sep 1, 2017

x + 1 x 3 − x \frac{x+1}{x^3-x} = x + 1 x ( x 2 − 1 ) \frac{x+1}{x(x^2-1)} = x + 1 x ( x + 1 ) ( x − 1 ) \frac{x+1}{x(x+1)(x-1)} = 1 x ( x − 1 ) \frac{1}{x(x-1)} = 1 x 2 − x \frac{1}{x^2-x}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Another way to eliminate Q, W, and T is to realise that in the original equation, when x=1, it is undefined. Q, W and T have a confirmed solution when x=1, eliminating them.

Kenny O. - 3 years, 9 months ago

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