Represent the following mixed infinite decimal periodic fractions as common fractions:
Simplify the following expressions.
((yy−x)−2−(x+y)2−4xyx2−xy)x4x2y2−y4
The given equation can be written as
[(x−yy)2−(x−y)2x(x−y)]x4y2(x2−y2) [since (x+y)2−4xy=(x−y)2]
⇒[(x−y)(x2−xy−y2)xy2][x4y2(x2−y2)]=x3(x2−xy−y2)y4(x+y)
⇒x3(x2−xy−y2)y4(x+y)=x5−x4y−x2y2xy4+y5