Question

Perfrom the indicated operation

c^2+4c/c^2-4 divided by 3c+12/c-2

Find answer if _____ is true

Answer 1

Answer: (6,0)

Explanation:

Answer 2

`(c)/(3(c+2))`

Explanation:

`(c^2+4c)/(c^2-4) / (3c+12)/(c-2)=(c^2+4c)/(c^2-4) * (c-2)/(3c+12)=((c^2+4c)(c-2))/((c^2-4)(3c+12))`

Factor
`c^2-4`:
`c^2-4=(c-2)(c+2)`

`\implies((c^2+4c)(c-2))/((c+2)(c-2)(3c+12))`

Cancel the common factor
`(c-2)`:

`\implies((c^2+4c))/((c+2)(3c+12))`

Factor
`c^2+4c`:
`c^2+4c=c(c+4)`

Factor
`3c+12`:
`3c+12=3(c+4)`

`\implies(c(c+4))/(3(c+2)(c+4))`

Cancel the common factor
`(c+4)`:

`\implies(c)/(3(c+2))`