Question

Упростите выражение
(x^2+7x+13)^2-(x^2-3x+7)^2/4x^2+8x+40*x/10x+6
при х=2014,8

Answer 1

$\frac{(x^2+7x+13)^2-(x^2-3x+7)^2}{4x^2+8x+40} * \frac{x}{10x+6}=$

$= \frac{((x^2+7x+13)-(x^2-3x+7))((x^2+7x+13)+(x^2-3x+7))}{4(x^2+2x+10)} * \frac{x}{10x+6}=$

$= \frac{(x^2+7x+13-x^2+3x-7)(x^2+7x+13+x^2-3x+7)}{4(x^2+2x+10)} * \frac{x}{10x+6}=$

$= \frac{(10x+6)(2x^2+4x+20)}{4(x^2+2x+10)} * \frac{x}{10x+6}=\frac{2(10x+6)(x^2+2x+10)}{4(x^2+2x+10)} * \frac{x}{10x+6}= \frac{x}{2} =$

$= \frac{2014,8}{2} =1007,4$