Simplify (x^3+9x^2-10x)/(x^3-9x^2-10x)

$\frac{x^{3} + 9 x^{2} - 10 x}{x^{3} - 9 x^{2} - 10 x}$

Simplify the numerator.

Factor $x$ out of $x^{3} + 9 x^{2} - 10 x$ .

Factor $x$ out of $x^{3}$ .

$\frac{x \cdot x^{2} + 9 x^{2} - 10 x}{x^{3} - 9 x^{2} - 10 x}$

Factor $x$ out of $9 x^{2}$ .

$\frac{x \cdot x^{2} + x (9 x) - 10 x}{x^{3} - 9 x^{2} - 10 x}$

Factor $x$ out of $- 10 x$ .

$\frac{x \cdot x^{2} + x (9 x) + x \cdot - 10}{x^{3} - 9 x^{2} - 10 x}$

Factor $x$ out of $x \cdot x^{2} + x (9 x)$ .

$\frac{x (x^{2} + 9 x) + x \cdot - 10}{x^{3} - 9 x^{2} - 10 x}$

Factor $x$ out of $x (x^{2} + 9 x) + x \cdot - 10$ .

$\frac{x (x^{2} + 9 x - 10)}{x^{3} - 9 x^{2} - 10 x}$

Factor $x^{2} + 9 x - 10$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 10$ and whose sum is $9$ .

$- 1, 10$

Write the factored form using these integers.

$\frac{x ((x - 1) (x + 10))}{x^{3} - 9 x^{2} - 10 x}$

$\frac{x (x - 1) (x + 10)}{x^{3} - 9 x^{2} - 10 x}$

Simplify the denominator.

Factor $x$ out of $x^{3} - 9 x^{2} - 10 x$ .

Factor $x$ out of $x^{3}$ .

$\frac{x (x - 1) (x + 10)}{x \cdot x^{2} - 9 x^{2} - 10 x}$

Factor $x$ out of $- 9 x^{2}$ .

$\frac{x (x - 1) (x + 10)}{x \cdot x^{2} + x (- 9 x) - 10 x}$

Factor $x$ out of $- 10 x$ .

$\frac{x (x - 1) (x + 10)}{x \cdot x^{2} + x (- 9 x) + x \cdot - 10}$

Factor $x$ out of $x \cdot x^{2} + x (- 9 x)$ .

$\frac{x (x - 1) (x + 10)}{x (x^{2} - 9 x) + x \cdot - 10}$

Factor $x$ out of $x (x^{2} - 9 x) + x \cdot - 10$ .

$\frac{x (x - 1) (x + 10)}{x (x^{2} - 9 x - 10)}$

Factor $x^{2} - 9 x - 10$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 10$ and whose sum is $- 9$ .

$- 10, 1$

Write the factored form using these integers.

$\frac{x (x - 1) (x + 10)}{x ((x - 10) (x + 1))}$

$\frac{x (x - 1) (x + 10)}{x (x - 10) (x + 1)}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x (x - 1) (x + 10)}{x (x - 10) (x + 1)}$

Rewrite the expression.

$\frac{(x - 1) (x + 10)}{(x - 10) (x + 1)}$

Simplify (x^3+9x^2-10x)/(x^3-9x^2-10x)

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