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].
