Question

Упростите выражение 9a-4/a+7 - 44-22a/a^2+5a-14

Answer 1

$\dfrac{9a-4}{a+7}-\dfrac{44-22a}{a^2+5a-14}=\dfrac{9a-4}{a+7}-\dfrac{44-22a}{a^2+7a-2a-14}=\dfrac{9a-4}{a+7}-\\ \\ -\dfrac{44-22a}{a(a+7)-2(a+7)}=\dfrac{9a-4}{a+7}-\dfrac{44-22a}{(a+7)(a-2)}=\\ \\ =\dfrac{(9a-4)(a-2)-44+22a}{(a+7)(a-2)}=\dfrac{9a^2-22a+8-44+22a}{(a+7)(a-2)}=\\ \\ =\dfrac{9a^2-36}{(a+7)(a-2)}=\dfrac{9(a^2-4)}{(a+7)(a-2)}=\dfrac{9(a-2)(a+2)}{(a+7)(a-2)}=\dfrac{9(a+2)}{a+7}$