Question

20 баллов. Сократите дробь
$displaystyle frac{(a+1)^2+1}{a^4+4};\ frac{9x^2+3x+1}{81x^4+9x^2+1};$

Answer 1

$frac{ (a+1)^{2}+1 }{a^4+4} = frac{a^2+2a+2}{(a^2+2)^2-4a^2} = frac{a^2+2a+2}{(a^2+2-2a)(a^2+2a+2)} = frac{1}{a^2-2a+2}$

$frac{9x^2+3x+1}{81x^4+9x^2+1} = frac{9x^2+3x+1}{(9x^2+1)^2-(3x)^2} = frac{9x^2+3x+1}{(9x^2+1-3x)(9x^2+1+3x)} = frac{1}{9x^2-3x+1}$