Question

Всем кто не спит

упростите выражение: y+c/c * (c/y+c/y+c)

Answer 1

$\dfrac{y+c}{c} \cdot \Big(\dfrac{c}{y}+\dfrac{c}{y+c}\Big)=\dfrac{y+c}{c}\cdot \dfrac{cy+c^{2}+cy }{y(y+c)} =\dfrac{c^{2}+2cy }{cy} =\\\\=\dfrac{c\cdot (c+2y)}{c\cdot y}=\boxed{\dfrac{c+2y}{y}}$

$2)\Big(\dfrac{c-d}{c^{2}+cd }-\dfrac{c}{d^{2}+cd }\Big) :\Big(\dfrac{d^{2} }{c^{3}-cd^{2}}+\dfrac{1}{c+d}\Big)=\\\\=\Big(\dfrac{c-d}{c(c+d)}-\dfrac{c}{d(c+d)}\Big):\Big(\dfrac{d^{2} }{c(c+d)(c-d)}+\dfrac{1}{c+d}\Big)=\\\\=\dfrac{cd-d^{2}-c^{2}}{cd(c+d)}:\dfrac{d^{2}+c^{2}-cd}{c(c+d)(c-d)} =-\dfrac{c^{2}+d^{2}-cd}{cd(c+d)} \cdot \dfrac{c(c+d)(c-d)}{c^{2}+d^{2}-cd}=\\\\=-\dfrac{c-d}{d}=\boxed{\dfrac{d-c}{d}}$