Question

Спростіть вираз а^2/ab-b^2+b/b-a

Answer 1

$\frac{a^2}{ab-b^2} + \frac{b}{b-a} = \frac{a^2}{b(a-b)} + \frac{b}{-(a-b)} = \frac{a^2}{b(a-b)} - \frac{b}{a-b} = \\ \\ = \frac{a^2-b^2}{b(a-b)} = \frac{(a-b)(a+b)}{b(a-b)} = \frac{a+b}{b} = \\ \\ = \frac{1}{b} (a+b) = \frac{a}{b} + \frac{b}{b} = \frac{a}{b} +1$