Question

Please help me....I really need help!!

Which expression is equal to
`(cx^(2)-4 )/(6c^(4)+15c^(3) )` ÷
`(c^(2) +4c+4)/(12c^(3)+30c^(2) )` ?

A.
`(2(c-2) )/(c(c-2))`
B.
`(2(c-2))/(c(c-2))`
C.
`(c(c+2))/(2(c+2))`

Answer 1

`(c^2-4)/(6c^4+15c^3)/(c^2+4c+4)/(12c^3+30c^2)=(c^2-2^2)/(3c^3(2c+5))/(c^2+2(c)(2)+2^2)/(6c^2(2c+5))\\\\_{\text{use}\ a^2-b^2=(a-b)(a+b)\ \text{and}\ (a+b)^2=a^2+2ab+b^2}\\\\=((c-2)(c+2))/(3c^3(2c+5))\cdot(6c^2(2c+5))/((c+2)^2)=((c-2))/(c)\cdot(2)/((c+2))=\boxed{(2(c-2))/(c(c+2))}`