Question

equivalent expression for 2log(x+1)-2log(x-1)-log(x-1)

Answer 1

Simplifying
2log(x + 1) + -2log(x + -1) + -1log(x + -1)

Reorder the terms:
2glo(1 + x) + -2log(x + -1) + -1log(x + -1)
(1 * 2glo + x * 2glo) + -2log(x + -1) + -1log(x + -1)
(2glo + 2glox) + -2log(x + -1) + -1log(x + -1)

Reorder the terms:
2glo + 2glox + -2glo(-1 + x) + -1log(x + -1)
2glo + 2glox + (-1 * -2glo + x * -2glo) + -1log(x + -1)
2glo + 2glox + (2glo + -2glox) + -1log(x + -1)

Reorder the terms:
2glo + 2glox + 2glo + -2glox + -1glo(-1 + x)
2glo + 2glox + 2glo + -2glox + (-1 * -1glo + x * -1glo)
2glo + 2glox + 2glo + -2glox + (1glo + -1glox)

Reorder the terms:
2glo + 2glo + 1glo + 2glox + -2glox + -1glox

Combine like terms: 2glo + 2glo = 4glo
4glo + 1glo + 2glox + -2glox + -1glox

Combine like terms: 4glo + 1glo = 5glo
5glo + 2glox + -2glox + -1glox

Combine like terms: 2glox + -2glox = 0
5glo + 0 + -1glox
5glo + -1glox

Answer 2

log [ (x+1)^2 /((x-1)^2(x-1)) ]
= log ((x+1)^2 / (x-1)^3 )