Question

a^3+a^2-a-1/a^2+2a+1 cкоротить

Answer 1

$\displaystyle \frac{a^3+a^2-a-1}{a^2+2a+1}=\frac{a^2(a+1)-(a+1)}{(a+1)^2}=\frac{(a+1)(a^2-1)}{(a+1)^2}=\\ \\ =\frac{(a+1)(a-1)(a+1)}{(a+1)^2}=\frac{(a+1)^2(a-1)}{(a+1)^2}=a-1$

Answer 2

$\frac{ {a}^{3} + {a}^{2} - a - 1}{ {a}^{2} + 2a + 1 } = \frac{a( {a}^{2} - 1) + ( {a}^{2} - 1) }{ {(a + 1)}^{2} } = \frac{(a + 1)( {a}^{2} - 1)}{ {(a + 1)}^{2} } = \frac{(a + 1)(a + 1)(a - 1)}{ {(a + 1)}^{2} } = a - 1$