Maths

Algebra Level 2

For all x x in the domain of the function x + 1 x 3 − x \dfrac{x+1}{x^3-x} , this function is equivalent to:

F. 1 x 2 − 1 x 3 \dfrac1{x^2} -\dfrac1{x^3}
G. 1 x 3 − 1 x \dfrac1{x^3} -\dfrac1x
H. 1 x 2 − 1 \dfrac1{x^2-1}
J. 1 x 2 − x \dfrac1{x^2-x}
K. 1 x 3 \dfrac1{x^3}

H F G K J

Anshuman Das by Anshuman Das , 19, India

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2 solutions

⇒ x + 1 x 3 − x \Rightarrow \dfrac{x+1}{x^3-x}

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

⇒ x + 1 x ( x + 1 ) ( x − 1 ) \Rightarrow \dfrac{x+1}{x(x+1)(x-1)}

⇒ 1 x 2 − x \Rightarrow \boxed{\dfrac{1}{x^2-x}}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Ondřej Chmelík
May 19, 2019

J is correct.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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