Simplify (x^3-20x^2+100x)/(x^3-10x^2)

$\frac{x^{3} - 20 x^{2} + 100 x}{x^{3} - 10 x^{2}}$

Simplify the numerator.

Factor $x$ out of $x^{3} - 20 x^{2} + 100 x$ .

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

$\frac{x \cdot x^{2} - 20 x^{2} + 100 x}{x^{3} - 10 x^{2}}$

Factor $x$ out of $- 20 x^{2}$ .

$\frac{x \cdot x^{2} + x (- 20 x) + 100 x}{x^{3} - 10 x^{2}}$

Factor $x$ out of $100 x$ .

$\frac{x \cdot x^{2} + x (- 20 x) + x \cdot 100}{x^{3} - 10 x^{2}}$

Factor $x$ out of $x \cdot x^{2} + x (- 20 x)$ .

$\frac{x (x^{2} - 20 x) + x \cdot 100}{x^{3} - 10 x^{2}}$

Factor $x$ out of $x (x^{2} - 20 x) + x \cdot 100$ .

$\frac{x (x^{2} - 20 x + 100)}{x^{3} - 10 x^{2}}$

Factor using the perfect square rule.

Rewrite $100$ as $10^{2}$ .

$\frac{x (x^{2} - 20 x + 10^{2})}{x^{3} - 10 x^{2}}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$20 x = 2 \cdot x \cdot 10$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 10$ .

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

Simplify terms.

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

Factor $x^{2}$ out of $x^{3}$ .

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

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

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

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

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

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $x {(x - 10)}^{2}$ .

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

Cancel the common factors.

Factor $x$ out of $x^{2} (x - 10)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of ${(x - 10)}^{2}$ and $x - 10$ .

Factor $x - 10$ out of ${(x - 10)}^{2}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - 10}{x}$

Simplify (x^3-20x^2+100x)/(x^3-10x^2)

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