Question

Упростите выражение 6c^3+3c/c^3-1 - 3c^2/c^2+c+1

Answer 1

$\frac{6c^{3}+3c }{c^{3}-1}-\frac{3c^{2}}{c^{2}+c+1 }=\frac{6c^{3}+3c}{(c-1)(c^{2}+c+1)}-\frac{3c^{2}}{c^{2}+c+1}=\frac{6c^{3}+3c-3c^{3}+3c^{2}}{(c-1)(c^{2}+c+1)}=\frac{3c^{3}+3c^{2}+3c}{(c-1)(c^{2}+c+1)}=\frac{3c(c^{2}+c+1)}{(c-1)(c^{2}+c+1)}=\frac{3c}{c-1} \\\\Otvet:\boxed{\frac{3c}{c-1}}$