Question 279768
{{{(3/2)(ln(x^2+1)-ln(x+1)-ln(x-1))}}}
We can use a property of logarithms, {{{log(a, (p)) - log(a, (q)) = log(a, (p/q))}}}, to combine the first two logarithms:
{{{(3/2)(ln((x^2+1)/(x+1))-ln(x-1))}}}
We can use that property again to combine the remaining logarithms:
{{{(3/2)(ln(((x^2+1)/(x+1))/(x-1)))}}}
which simplifies as follows:
{{{(3/2)(ln((x^2+1)/((x+1)*(x-1))))}}}
{{{(3/2)(ln((x^2+1)/(x^2-1)))}}}
This is a single term and may be an acceptable answer. But your teacher probably wants you to use another property of logarithms, {{{q*log(a, (p)) = log(a, (p^q))}}}, to move the 3/2 from in front into the argument as an exponent:
{{{ln(((x^2+1)/(x^2-1))^(3/2))}}}