Question

{x}^{2}  ×( \frac{x}{y} - \frac{y}{x}) \times ( \frac{y}{x} + \frac{x}{y} ) \times {y}^{2}x2 ×(yx​−xy​)×(xy​+yx​)×y2​

Answer 1

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Answer 2

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Answer:

Knowing that (a+b)2−(a−b)2=4ab, I’d note right away that the denominator is

(x−y)2−(x+y)2x2−y2=−4xyx2−y2,

so we have

−(x2−y2)24xy(x2+y2)+x2+y24xy=(x2+y2)2−(x2−y2)24xy(x2+y2)=4x2y24xy(x2+y2)=xyx2+y2.