simplify (x^3-x)/x — step-by-step solution

Let's reduce:

\frac{x^{3} - x}{x}

We first try to factorize the numerator

Let's factor in

ℝ

x^{3} - x

You can factorize this expression into:

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

Let's factor in

ℝ

(x^{2} - 1)

Factors found:

(x + 1) \cdot (x - 1)

With the new factorized numerator, we try to simplify the new quotient:

\frac{x \cdot (x + 1) \cdot (x - 1)}{x}

(x + 1) \cdot (x - 1)

x \cdot x

+ x \cdot -1

+ 1 \cdot x

+ 1 \cdot -1

x^{2}

- x

+ x

- 1

x^{2} + 0 - 1

▷Answer: $x^{2} - 1$