Question

calcule a fração 2x+1/x+1 - x-1/x^2-1

Answer 1

Olá!

$\\ \displaystyle \mathsf{\frac{2x + 1}{x + 1} - \frac{x - 1}{x^2 - 1} =} \\\\\\ \mathsf{\frac{2x + 1}{x + 1} - \frac{x - 1}{(x + 1)(x - 1)} =} \\\\\\ \mathsf{\frac{(2x + 1) \cdot (x - 1) - (x - 1) \cdot 1}{(x + 1)(x - 1)} =} \\\\\\ \mathsf{\frac{2x^2 - 2x + x - 1 - x + 1}{(x + 1)(x - 1)} =} \\\\\\ \mathsf{\frac{2x^2 - 2x}{(x + 1)(x - 1)} =} \\\\\\ \mathsf{\frac{2x(x - 1)}{(x + 1)(x - 1)} =} \\\\\\ \boxed{\mathsf{\frac{2x}{x + 1}}}$