Question

Спростіть вираз а^2/ab-b^2+b/b-a

Answer 1

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