Simplify. $$ \frac{x^{3}-6 x^{2}+9 x}{x^{3}-3 x^{2}} $$ $$ \frac{x^{3}-6 x^{2}+9 x}{x^{3}-3 x^{2}}=\square $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{x^{3}-6 x^{2}+9 x}{x^{3}-3 x^{2}}
$$

**Step 1: Factor the Numerator and Denominator**

**Numerator:**
$$
x^{3} - 6x^{2} + 9x = x(x^{2} - 6x + 9) = x(x - 3)^2
$$

**Denominator:**
$$
x^{3} - 3x^{2} = x^{2}(x - 3)
$$

**Step 2: Simplify the Expression**

Now, substitute the factored forms back into the original expression:

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

Cancel out the common factors:

- **Cancel $$ x $$ in the numerator and denominator:**
$$
\frac{\cancel{x}(x - 3)^2}{x^{\cancel{2}}(x - 3)} = \frac{(x - 3)^2}{x(x - 3)}
$$

- **Cancel one $$ (x - 3) $$ from the numerator and denominator:**
$$
\frac{\cancel{(x - 3)}(x - 3)}{x \cancel{(x - 3)}} = \frac{x - 3}{x}
$$

**Final Simplified Form:**
$$
\frac{x - 3}{x}
$$

Answer:
$$
\frac{x^{3}-6 x^{2}+9 x}{x^{3}-3 x^{2}} = \frac{x - 3}{x}
$$
$$ \frac{x - 3}{x} $$

Simplify. \[ \frac{x^{3}-6 x^{2}+9 x}{x^{3}-3 x^{2}} \] \( \frac{x^{3}-6 x^{2}+9 x}{x^{3}-3 x^{2}}=\square \)