Expand (x/y - 3)(y + 1/4): Binomial Multiplication with Fractions

To solve the problem, we will use the distributive property to expand and simplify the expression $(\frac{x}{y}-3)(y+\frac{1}{4})$.

• Step 1: Apply the distributive property to each term in the first expression with each term in the second.

The expression $(\frac{x}{y})(y + \frac{1}{4}) - 3(y + \frac{1}{4})$ needs to be expanded:

• Step 2: Distribute $\frac{x}{y}$ across $y$ and $\frac{1}{4}$.

$\frac{x}{y} \cdot y = x.$
$\frac{x}{y} \cdot \frac{1}{4} = \frac{x}{4y}.$

• Step 3: Distribute $-3$ across $y$ and $\frac{1}{4}$.

$-3 \cdot y = -3y.$
$-3 \cdot \frac{1}{4} = -\frac{3}{4}.$

• Step 4: Combine all distributed terms.

The complete expanded expression becomes:

$x + \frac{x}{4y} - 3y - \frac{3}{4}.$

Therefore, the solution to the problem is $\boxed{x+\frac{x}{4y}-3y-\frac{3}{4}}$.