Question

сократить дробь
a^3-27/5a^2-16a+3

Answer 1

 Преобразуем знаменатель дроби.   5a^2-16a+3=0.   D=256-4*5*3=256-60=196=14^2.
a1=(16+14)/1030/10=3. a2=(16-14)/10=2/10=1/5.
5a^2-16a+3=5(a-3)*(a-1/5)=(a-3)(5a-1)
(a-3)(a^2+3a+9)/a-3)(5a-1)=(a^2+3a+9)/(5a-1)

Answer 2

$\frac{a^3-27}{5a^2-16a+3} \\ 5a^2-16a+3 \\ \frac{D}{4}=64-15=49=7^2 \\ a_1=\frac{8-7}{5}=\frac{1}{5} \\ a_2=\frac{8+7}{5}=3 \\ 5a^2-16a+3=5(a-\frac{1}{5})(a-3) \\ \\ \frac{a^3-27}{5(a-\frac{1}{5})(a-3)}= \frac{(a-3)(a^2+3a+9)}{5(a-\frac{1}{5})(a-3)}= \frac{a^2+3a+9}{5a-1}$