Question

Simplifique a expressão a+b/a^-1+b^-1 com a diferente de -b, a diferente de 0 e b diferente de 0

Answer 1

Olá!

$\\ \mathsf{\frac{a + b}{a^{- 1} + b^{- 1}} =} \\\\\\ \mathsf{\frac{a + b}{\frac{1}{a} + \frac{1}{b}} =} \\\\\\ \mathsf{\frac{a + b}{\frac{b + a}{ab}} =} \\\\\\ \mathsf{(a + b) \times \frac{ab}{b + a} =} \\\\\\ \mathsf{\frac{a + b}{b + a} \times ab =} \\\\ \boxed{\mathsf{ab}}$