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Question
Simplify `(x^3)/(x - y) + (y^3)/(y - x)`
Solution
`(x^3)/(x - y) + (y^3)/(y - x)`
= `(x^3)/(x - y) - y^3/(-1(x - y))`
= `(x^3)/(x - y) - (y^3)/(x - y)`
= `(x^3 - y^3)/(x - y)` ...(using a3 – b3 = (a – b) (a2 + ab + b2))
= `((x - y)(x^2 + xy + y^2))/(x - y)`
= x2 + xy + y2
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