chahanamoktan175 chahanamoktan175
  • 01-03-2021
  • Mathematics
contestada

a/ab-bsquare + b/ab-asquare?​

Respuesta :

Muscardinus Muscardinus
  • 06-03-2021

Answer:

[tex]\dfrac{(a+b)}{ab}[/tex]

Step-by-step explanation:

The given expression is :

[tex]\dfrac{a}{ab-b^2}+\dfrac{b}{ab-a^2}[/tex]

It can be solved as follows :

[tex]\dfrac{a}{ab-b^2}+\dfrac{b}{ab-a^2}=\dfrac{a}{b(a-b)}+\dfrac{b}{a(b-a)}\\\\=\dfrac{a}{b(a-b)}+\dfrac{b}{-a(-b+a)}\\\\=\dfrac{1}{a-b}(\dfrac{a}{b}-\dfrac{b}{a})\\\\=\dfrac{a^2-b^2}{ab(a-b)}\\\\=\dfrac{(a-b)(a+b)}{ab(a-b)}\\\\=\dfrac{(a+b)}{ab}[/tex]

So, the solution of the given expression is equal to [tex]\dfrac{(a+b)}{ab}[/tex].

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