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Réponse :

Explications étape par étape

Bonjour

Simplifier

A = (x^2 - y^2)/(y^2 + xy)

A = (x - y)(x + y) / [y(y + x)]

A = (x - y)/y

B = (x + y)/(x - y) + y^2/(x - y)^2

B = [(x + y)(x - y) + y^2]/(x - y)^2

B = (x^2 - y^2 + y^2)/(x - y)^2

B = x^2/(x - y)^2

C = (x^2 - y^2)/(xy) + (xy - y^2)/(xy - x^2)

C = [(x - y)(x + y)]/(xy) + [y(x - y)]/[x(y - x)]

C = [(x - y)(x + y)(y - x) + y(x - y)y]/[xy(y - x)]

C = [(x - y)(y^2 - x^2 + y^2]/[xy(y - x)]

C = -(2y^2 - x^2)/(xy)

C = (x^2 - 2y^2)/(xy)

D = (x - y + (2y^2)/(x + y))/((x + y)/(2xy) + 1/(x + y))

D = [(x - y)(x + y) + 2y^2]/(x + y) / [(x + y)(x + y) + 2xy]/[(2xy(x + y)]

D = (x^2 - y^2 + 2y^2)/(x + y) / (x^2 + 2xy + y^2 + 2xy)/(2xy(x + y))

D = (x^2 + y^2)/(x + y) / (x^2 + y^2 + 4xy)/(2xy(x + y)

D = (x^2 + y^2)/(x + y) * (2xy(x + y))/(x^2 + y^2 + 4xy)

D = [2xy(x^2 + y^2)] / [4xy + x^2 + y^2]