Simplify (x^3-24x^2+144x)/(x^3-12x^2)

$\frac{x^{3} - 24 x^{2} + 144 x}{x^{3} - 12 x^{2}}$

Simplify the numerator.

Factor $x$ out of $x^{3} - 24 x^{2} + 144 x$ .

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

$\frac{x \cdot x^{2} - 24 x^{2} + 144 x}{x^{3} - 12 x^{2}}$

Factor $x$ out of $- 24 x^{2}$ .

$\frac{x \cdot x^{2} + x (- 24 x) + 144 x}{x^{3} - 12 x^{2}}$

Factor $x$ out of $144 x$ .

$\frac{x \cdot x^{2} + x (- 24 x) + x \cdot 144}{x^{3} - 12 x^{2}}$

Factor $x$ out of $x \cdot x^{2} + x (- 24 x)$ .

$\frac{x (x^{2} - 24 x) + x \cdot 144}{x^{3} - 12 x^{2}}$

Factor $x$ out of $x (x^{2} - 24 x) + x \cdot 144$ .

$\frac{x (x^{2} - 24 x + 144)}{x^{3} - 12 x^{2}}$

Factor using the perfect square rule.

Rewrite $144$ as $12^{2}$ .

$\frac{x (x^{2} - 24 x + 12^{2})}{x^{3} - 12 x^{2}}$

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

$24 x = 2 \cdot x \cdot 12$

Rewrite the polynomial.

$\frac{x (x^{2} - 2 \cdot x \cdot 12 + 12^{2})}{x^{3} - 12 x^{2}}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 12$ .

$\frac{x {(x - 12)}^{2}}{x^{3} - 12 x^{2}}$

Simplify terms.

Factor $x^{2}$ out of $x^{3} - 12 x^{2}$ .

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

$\frac{x {(x - 12)}^{2}}{x^{2} x - 12 x^{2}}$

Factor $x^{2}$ out of $- 12 x^{2}$ .

$\frac{x {(x - 12)}^{2}}{x^{2} x + x^{2} \cdot - 12}$

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot - 12$ .

$\frac{x {(x - 12)}^{2}}{x^{2} (x - 12)}$

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

Factor $x$ out of $x {(x - 12)}^{2}$ .

$\frac{x ({(x - 12)}^{2})}{x^{2} (x - 12)}$

Cancel the common factors.

Factor $x$ out of $x^{2} (x - 12)$ .

$\frac{x ({(x - 12)}^{2})}{x (x (x - 12))}$

Cancel the common factor.

$\frac{x {(x - 12)}^{2}}{x (x (x - 12))}$

Rewrite the expression.

$\frac{{(x - 12)}^{2}}{x (x - 12)}$

Cancel the common factor of ${(x - 12)}^{2}$ and $x - 12$ .

Factor $x - 12$ out of ${(x - 12)}^{2}$ .

$\frac{(x - 12) (x - 12)}{x (x - 12)}$

Cancel the common factors.

Factor $x - 12$ out of $x (x - 12)$ .

$\frac{(x - 12) (x - 12)}{(x - 12) x}$

Cancel the common factor.

$\frac{(x - 12) (x - 12)}{(x - 12) x}$

Rewrite the expression.

$\frac{x - 12}{x}$

Simplify (x^3-24x^2+144x)/(x^3-12x^2)

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