Simplify the expression completel \[ \frac{x^{3}-4 x^{2}}{x^{2}-5 x+4} \]

To simplify the expression \(\frac{x^{3}-4 x^{2}}{x^{2}-5 x+4}\), we can start with factorization. First, factor the numerator \(x^{3}-4 x^{2}\): \[ x^{2}(x - 4) \] Now, for the denominator \(x^{2}-5 x+4\), we look for two numbers that multiply to \(4\) and add up to \(-5\). The numbers are \(-4\) and \(-1\). Thus, we can factor the denominator as: \[ (x - 4)(x - 1) \] Now we can rewrite the original expression with the factored forms: \[ \frac{x^{2}(x - 4)}{(x - 4)(x - 1)} \] Next, we can cancel the common factor \((x - 4)\) from the numerator and the denominator (note that \(x \neq 4\)): \[ \frac{x^{2}}{x - 1} \] Thus, the simplified expression is: \[ \frac{x^{2}}{x - 1} \quad (x \neq 4) \]