Question

найти значения выражения

 

$<var>\frac{40x^3+160x^2-360x-1440}{2x^2+5x-12}</var>$

 

 

 

при x =6.5

Answer 1

$<var>\frac{40x^3+160x^2-360x-1440}{2x^2+5x-12}=\frac{40x^2(x+4)-360(x+4)}{2(x^2-1.5x+4x-6)}=\\ =\frac{(40x^2-360)(x+4)}{2((x^2+4x)-(1.5x+6))}=\frac{40(x^2-9)(x+4)}{2(x(x+4)-1.5(x+4))}=\frac{40(x^2-9)(x+4)}{2((x-1.5)(x+4)}=\\ =\frac{20(x^2-9)}{(x-1.5)}\\ \frac{20(x^2-9)}{(x-1.5)}=\frac{20(6.5^2-9)}{(6.5-1.5)}=\frac{20*33.25}{5}=133</var>$