Question

спростити вираз a+4/a^2-6a+9 : a^2-16/ a-3 - 2/a-4

Answer 1

$\displaystyle\bf\\\frac{a+4}{a^{2}-6a+9 }:\frac{a^{2}-16 }{a-3} -\frac{2}{a-4} =\frac{a+4}{(a-3)^{2} }:\frac{(a-4)(a+4)}{a-3} -\frac{2}{a-4}=\\\\\\=\frac{a+4}{(a-3)^{2} }\cdot\frac{a-3}{(a-4)(a+4)} -\frac{2}{a-4}=\frac{1}{(a-3)(a-4)}-\frac{2}{a-4}=\\\\\\= \frac{1-2\cdot(a-3)}{(a-3)(a-4)} =\frac{1-2a+6}{(a-3)(a-4)} =\frac{7-2a}{(a-3)(a-4)}$