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Question Number 202383 by MATHEMATICSAM last updated on 25/Dec/23

Show that ((a(√b) − b(√a))/(a(√b) + b(√a))) = (1/(a − b))(a + b − 2(√(ab))).

Showthatab−baab+ba=1a−b(a+b−2ab).

Answered by deleteduser1 last updated on 25/Dec/23

=(((a(√b)−b(√a))^2 )/(ab(a−b))) =((a^2 b+b^2 a−2ab(√(ab)))/(ab(a−b)))=((a+b−2(√(ab)))/(a−b))

=(ab−ba)2ab(a−b)=a2b+b2a−2ababab(a−b)=a+b−2aba−b

Answered by lorance last updated on 25/Dec/23

((a(√b) − b(√a))/(a(√b) + b(√a))) = (((√(ab))×((√a)−(√b)))/( (√(ab))×((√a)+(√b))))×(((√a)−(√b))/( (√a)−(√b)))=((((√a)−(√b))^2 )/( ((√a))^2 −((√b))^2 ))=(1/(a−b))×(a+b−2(√(ab)))

ab−baab+ba=ab×(a−b)ab×(a+b)×a−ba−b=(a−b)2(a)2−(b)2=1a−b×(a+b−2ab)

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