Question

Решите пример см. картинку

Answer 1

$\dfrac{4a+4}{a-2}$

Объяснение:

$1) \ \dfrac{a+2}{2-a}-\dfrac{2-a}{2+a}=\dfrac{(a+2)^{2}-(2-a)^{2}}{(2-a)(2+a)}=\dfrac{a^{2}+4a+4-(4-4a+a^{2})}{2^{2}-a^{2}}=$

$=\dfrac{a^{2}+4a+4-4+4a-a^{2}}{4-a^{2}}=\dfrac{8a}{4-a^{2}} \ ;$

$2) \ \dfrac{8a}{4-a^{2}}-\dfrac{4a^{2}}{a^{2}-4}=\dfrac{8a}{4-a^{2}}- \bigg (-\dfrac{4a^{2}}{4-a^{2}} \bigg )=\dfrac{8a}{4-a^{2}}+\dfrac{4a^{2}}{4-a^{2}}=\dfrac{4a^{2}+8a}{4-a^{2}} \ ;$

$3) \ \dfrac{1}{a^{3}+a^{2}}-\dfrac{1-a}{a^{2}}=\dfrac{1}{a^{2}(a+1)}-\dfrac{1-a}{a^{2}}=\dfrac{1-(1-a)(1+a)}{a^{2}(a+1)}=\dfrac{1-(1-a^{2})}{a^{2}(a+1)}=$

$=\dfrac{1-1+a^{2}}{a^{2}(a+1)}=\dfrac{a^{2}}{a^{2}(a+1)}=\dfrac{1}{a+1} \ ;$

$4) \ \dfrac{1}{a+1}-1=\dfrac{1}{a+1}-\dfrac{a+1}{a+1}=\dfrac{1-(a+1)}{a+1}=\dfrac{1-a-1}{a+1}=\dfrac{-a}{a+1} \ ;$

$5) \ \dfrac{4a^{2}+8a}{4-a^{2}}:\dfrac{-a}{a+1}=\dfrac{4a^{2}+8a}{4-a^{2}} \cdot \dfrac{a+1}{-a}=-\dfrac{a(4a+8)(a+1)}{a(4-a^{2})}=-\dfrac{(4a+8)(a+1)}{4-a^{2}}=$

$=-\dfrac{4(a+2)(a+1)}{(2-a)(2+a)}=-\dfrac{4(a+1)}{2-a}=-\dfrac{4a+4}{2-a}=\dfrac{4a+4}{a-2} \ ;$