Question Number 105023 by bemath last updated on 25/Jul/20

(((x^2 −y^2 )^2 )/((1−x^2 )(y^2 −1)))+(((1−x^2 )^2 )/((x^2 −y^2 )(y^2 −1)))+(((y^2 −1)^2 )/((1−x^2 )(x^2 −y^2 )))=

Answered by john santu last updated on 25/Jul/20

(((x^2 −y^2 )^3 +(1−x^2 )^3 +(y^2 −1)^3 )/((1−x^2 )(y^2 −1)(x^2 −y^2 )))  [ set (x^2 −y^2 ) = u ; (1−x^2 ) = v ;  (y^2 −1) = w ]   ⇔((u^3 +v^2 +w^3 )/(uvw)) = (((u+w)^3 −3uw(u+w)+v^3 )/(uvw))  [ u+w = x^2 −1 = −v ]  ⇒((−v^3 +3uvw+v^3 )/(uvw)) = ((3uvw)/(uvw)) = 3  (JS ★♠)