Question

Сократить a) x^3-27/7x-21 б) am-an-4m+4n/16-a^2

Answer 1

$\displaystyle\bf\\1)\\\\\frac{x^{3} -27}{7x-21} =\frac{x^{3}-3^{3} }{7\cdot(x-3)} =\frac{(x-3)\cdot(x^{2} +3x+9)}{7\cdot(x-3)} =\frac{x^{2} +3x+9}{7} \\\\\\2)\\\\\frac{am-an-4m+4n}{16-a^{2} } =\frac{(am-an)-(4m-4n)}{4^{2} -a^{2} } =\\\\\\=\frac{a\cdot(m-n)-4\cdot(m-n)}{(4-a)\cdot(4+a)} =\frac{(m-n)\cdot(a-4)}{(4-a)\cdot(4+a)} =\\\\\\=-\frac{m-n}{4+a} =\frac{n-m}{a+4}$