Question

I solved the problem i just don’t know what n cannot equal to

Answer 1

Recall that:

`\begin{gathered} \text{If b}\\e0\text{ we get that:} \\ (ab)/(cb)=(a)/(c)\text{.} \end{gathered}`

Notice that:

`\begin{gathered} 20n-16=4(5n-4), \\ 4n^2-4n^3=4n^2(1-n)=-4n^2(n-1), \\ 10n-10=10(n-1)\text{.} \end{gathered}`

Therefore:

`(20n-16)/(5n-4)\cdot(4n^2-4n^3)/(10n-10)=(4(5n-4))/(5n-4)\cdot(-4n^2(n-1))/(10(n-1))\text{.}`

Assuming that 5n-4≠0 and n-1≠0 we get:

`(4(5n-4))/(5n-4)\cdot(-4n^2(n-1))/(10(n-1))=4\cdot(-4n^2)/(10)\text{.}`

Simplifying the above result we get:

`4\cdot(-4n^2)/(10)=-(8n^2)/(5)\text{.}`

Now, the restrictions are 5n-4≠0 and n-1≠0, therefore:

`\begin{gathered} 5n-4\\e0\rightarrow5n\\e4\rightarrow n\\e(4)/(5), \\ n-1\\e0\rightarrow n\\e1. \end{gathered}`

Answer:

`\begin{gathered} -(8n^2)/(5), \\ \text{For }n\\e1\text{ and }n\\e(4)/(5). \end{gathered}`