Question

Упростите выражение: x^2+2x+2y^2-y^4/ x^2 -xy^2+2y^2-4

Answer 1

$frac{ x^{2} +2x+2y^{2} - y^{4} }{ x^{2} -xy^{2} +2y^{2} -4} = frac{( x^{2} - y^{4} )+2(x+ y^{2} )}{( x^{2} -4)- y^{2}(x-2) }= frac{(x+ y^{2} )(x- y^{2})+2(x+y^{2}) }{(x-2)(x+2)- y^{2}(x-2) } = \ frac{(x+ y^{2})(x- y^{2}+2) }{(x-2)(x- y^{2} +2)} = frac{x+ y^{2} }{x-2}$