Question

50б сделайте пожалуйста​

Answer 1

Ответ.

$1)\ \ \dfrac{a+18}{a^2-36}-\dfrac{1}{a^2-36}\cdot \dfrac{(a+6)^2}{a}=\dfrac{a+18}{(a-6)(a+6)}-\dfrac{1}{(a-6)(a+6)}\cdot \dfrac{(a+6)^2}{a}=\\\\\\=\dfrac{a+18}{(a-6)(a+6)}-\dfrac{a+6}{(a-6)\cdot a}=\dfrac{(a+18)\cdot a-(a+6)^2}{a\cdot (a-6)(a+6)}=\\\\\\=\dfrac{a^2+18a-a^2-12a-36}{a\cdot (a-6)(a+6)}=\dfrac{6a-36}{a\cdot (a-6)(a+6)}=\dfrac{6(a-6)}{a\cdot (a-6)(a+6)}=\dfrac{6}{a\, (a+6)}$

$2)\ \ \Big(\dfrac{2xy}{y^2-16x^2}-\dfrac{x}{y-4x}\Big):\dfrac{x^2}{y^2+4xy}=\\\\\\=\Big(\dfrac{2xy}{(y-4x)(y+4x)}-\dfrac{x}{y-4x}\Big):\dfrac{x^2}{y\, (y+4x)}=\\\\\\=\dfrac{2xy-x\, (y+4x)}{(y-4x)(y+4x)}:\dfrac{x^2}{y\, (y+4x)}=\dfrac{xy-4x^2}{(y-4x)(y+4x)}\cdot \dfrac{y\, (y+4x)}{x^2}=\\\\\\=\dfrac{x(y-4x)}{(y-4x)(y+4x)}\cdot \dfrac{y\, (y+4x)}{x^2}=\dfrac{xy}{x^2}=\dfrac{y}{x}$