Question

Resolva a expressão


$\frac{x + 1}{x} \div \frac{ {x }^{2} + 2x + 1} { {x}^{2} } - \frac{ {x }^{2} - 1 } {( {x + 1)}^{2} }^{?}$
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Answer 1

Explicação passo-a-passo:

$\sf \dfrac{x+1}{x}\div\dfrac{x^2+2x+1}{x^2}-\dfrac{x^2-1}{(x+1)^2}$

$\sf \dfrac{x+1}{x}\div\dfrac{(x+1)\cdot(x+1)}{x^2}-\dfrac{(x+1)\cdot(x-1)}{(x+1)\cdot(x+1)}$

$\sf =\dfrac{x+1}{x}\cdot\dfrac{x^2}{(x+1)\cdot(x+1)}-\dfrac{x-1}{x+1}$

$\sf =\dfrac{(x+1)\cdot x^2}{(x+1)\cdot x\cdot(x+1)}-\dfrac{x-1}{x+1}$

$\sf =\dfrac{x}{x+1}-\dfrac{x-1}{x+1}$

$\sf =\dfrac{x-(x-1)}{x+1}$

$\sf =\dfrac{x-x+1}{x+1}$

$\sf =\red{\dfrac{1}{x+1}}$