f(x)= ln(1+1/x) + ln((x-1)/(x+2)) can be written in the form ln(P(x)) - ln(Q(x)), whe

[nicole_]

f(x)= ln(1+1/x) + ln((x-1)/(x+2))

[FONT=&quot]On its maximal domain the function can be rewritten in the form
f(x) = ln(P(x))-ln(Q(x)), where P(x) and Q(x) are polynomials such that P(x) is of degree 2 and has constant term equal to -1.

Find P(x) and Q(x).

I do not understand how can I find the maximal domain and then rewrite the function.[/FONT]

 

[stapel]

f(x)= ln(1+1/x) + ln((x-1)/(x+2))

On its maximal domain the function can be rewritten in the form
f(x) = ln(P(x))-ln(Q(x)), where P(x) and Q(x) are polynomials such that P(x) is of degree 2 and has constant term equal to -1.

Find P(x) and Q(x).

I do not understand how can I find the maximal domain and then rewrite the function.

Is there another part to this exercise, where they ask you for that maximal domain? If not, then you don't need to "find" it; just be aware that it exists.

As for finding the polynomials, I would suggest that you start by using log rules (here) to split the two logs into two terms each. Then see about rearranging those log terms (combining them back together) to get polynomials of the specified sort.

Hint: (x + 1)(x - 1) = x^2 - 1 :wink: