Question

$\frac{ a^{2} - b^{2}}{ \sqrt{ (a-b)^{2}+4ab } }$ é equivalente a...?

Answer 1

Olá Yuri, boa noite!

$\\ \displaystyle \mathsf{\frac{a^2 - b^2}{\sqrt{(a - b)^2 + 4ab}} =} \\\\\\ \mathsf{\frac{(a + b) \cdot (a - b)}{\sqrt{(a^2 - 2ab + b^2) + 4ab}} =} \\\\\\ \mathsf{\frac{(a + b)(a - b)}{\sqrt{a^2 + 2ab + b^2}} =} \\\\\\ \mathsf{\frac{(a + b)(a - b)}{\sqrt{(a + b)^2}} =}\\\\\\\mathsf{\frac{(a + b)(a - b)}{(a + b)} =} \\\\ \boxed{\mathsf{a - b}}$