Simplify :
`(y^(3) - 5y^(2)) div y xx (y-1)`

Answer

To simplify the expression \((y^3 - 5y^2) \div (y \cdot (y - 1))\), we will follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{y^3 - 5y^2}{y \cdot (y - 1)} \]

### Step 2: Factor the numerator
The numerator \(y^3 - 5y^2\) can be factored by taking out the common factor \(y^2\):
\[ y^2(y - 5) \]
So, we can rewrite the expression as:
\[ \frac{y^2(y - 5)}{y \cdot (y - 1)} \]

### Step 3: Cancel common factors
Now, we can cancel the common factor \(y\) from the numerator and the denominator:
\[ \frac{y^2}{y} \cdot \frac{(y - 5)}{(y - 1)} = y \cdot \frac{(y - 5)}{(y - 1)} \]

### Step 4: Multiply the remaining terms
Now, we multiply \(y\) with the remaining fraction:
\[ y \cdot \frac{(y - 5)}{(y - 1)} = \frac{y(y - 5)}{(y - 1)} \]

### Step 5: Final expression
The simplified expression is:
\[ \frac{y(y - 5)}{(y - 1)} \]

### Summary of the solution
Thus, the simplified form of the given expression \((y^3 - 5y^2) \div (y \cdot (y - 1))\) is:
\[ \frac{y(y - 5)}{(y - 1)} \]