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skelet666 [1.2K]
3 years ago
5

A/ab-bsquare + b/ab-asquare?​

Mathematics
1 answer:
lord [1]3 years ago
7 0

Answer:

\dfrac{(a+b)}{ab}

Step-by-step explanation:

The given expression is :

\dfrac{a}{ab-b^2}+\dfrac{b}{ab-a^2}

It can be solved as follows :

\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}

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

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