Question

скоротити дріб(через дискримінант)​

Answer 1

$\displaystyle 1)\frac{a^3-27}{5a^2-16a+3}=\frac{(a-3)(a^2+3a+9)}{5a^2-a-15a+3}=\frac{(a-3)(a^2+3a+9)}{a(5a-1)-3(5a-1)}=\frac{(a-3)(a^2+3a+9)}{(5a-1)(a-3)}=\\\frac{a^2+3a+9}{5a-1}$

$\displaystyle 2)\frac{25-x^2}{x^2-6x+5}=\frac{(5-x)(5+x)}{x^2-x-5x+5}=\frac{-(x-5)(5+x)}{x(x-1)-5(x-1)}=\frac{-(x-5)(5+x)}{(x-1)(x-5)}=\\\\\frac{-(5+x)}{x-1}=-\frac{5+x}{x-1}$