Questions: (x-y)^2/(x+y) * (3x+3y)/(y^2-y^2) solve Domain

Solution Steps

We start with the given rational expressions: \[ \frac{(x-y)^{2}}{x+y} \quad \text{and} \quad \frac{3x+3y}{y^{2}-y^{2}} \]

The second expression has a denominator of \(y^{2} - y^{2}\), which simplifies to \(0\). This indicates that the expression is undefined for all values of \(y\), leading to a division by zero.

Despite the second expression being undefined, we can still multiply the numerators: \[ \text{Numerator: } 3x + 3y = 3(x + y) \] Thus, the multiplication of the two expressions results in: \[ \frac{(x-y)^{2} \cdot 3(x+y)}{0} \]

The overall expression simplifies to: \[ \frac{3(x-y)^{2}(x+y)}{0} \] Since the denominator is \(0\), the entire expression is undefined, leading to the conclusion that the result is: \[ \text{Simplified: } \text{zoo} \cdot (x - y)^{2} \cdot (x + y) \] This indicates that the expression does not have a valid value in its domain due to the division by zero.

Final Answer