Math Snap

STEP 1

1. The expression is a rational function.
2. The goal is to simplify the expression by canceling common factors in the numerator and the denominator.

STEP 2

1. Factor the numerator $x^{3} - 4x^{2} + 4x$.
2. Factor the denominator $x^{3} - 2x^{2}$.
3. Simplify the expression by canceling common factors.

STEP 3

Factor the numerator $x^{3} - 4x^{2} + 4x$.
First, factor out the greatest common factor (GCF), which is $x$:
$$x(x^{2} - 4x + 4)$$ Next, factor the quadratic $x^{2} - 4x + 4$. Notice it is a perfect square trinomial:
$$x(x - 2)^{2}$$

STEP 4

Factor the denominator $x^{3} - 2x^{2}$.
Factor out the greatest common factor (GCF), which is $x^{2}$:
$$x^{2}(x - 2)$$

Simplify the expression by canceling common factors.
The expression is:
$$\frac{x(x - 2)^{2}}{x^{2}(x - 2)}$$ Cancel the common factors $x$ and $x - 2$:
$$\frac{(x - 2)}{x}$$ The simplified expression is:
$$\frac{x - 2}{x}$$