Questions: 3(x-y)^2 / 5 : (10x-10y) / (x+y)

Solution Steps

To solve the given expression, we need to simplify the ratio of two fractions. The expression can be interpreted as a division of two fractions. We will first simplify each fraction separately and then perform the division.

Given the first fraction: \[ \frac{3(x-y)^2}{5} \]

Given the second fraction: \[ \frac{10(x-y)}{x+y} \]

To divide the two fractions, we multiply the first fraction by the reciprocal of the second fraction: \[ \frac{\frac{3(x-y)^2}{5}}{\frac{10(x-y)}{x+y}} = \frac{3(x-y)^2}{5} \times \frac{x+y}{10(x-y)} \]

Simplify the resulting expression: \[ \frac{3(x-y)^2 \cdot (x+y)}{5 \cdot 10(x-y)} = \frac{3(x-y) \cdot (x+y)}{50} \]

Final Answer