Question 869890
?

The right hand side,
{{{(a/(x+1))((x-1)/(x-1)) + ((b/(x-1)))((x+1)/(x+1))}}}
{{{(a(x-1)+b(x+1))/((x+1)(x-1))}}}
{{{(ax-a+bx+b)/(x^2-1)}}}


Now, the numerators of left and right are the same.  We started with the equality, so now just adjust numerators to same form and compare corresponding terms.


{{{ax+b=ax-a+bx+b}}}
{{{ax+b=ax+bx+b-a}}}
{{{ax+b=(a+b)x+(b-a)}}}


The way those correspond, 
{{{a=a+b}}} and {{{b=b-a}}}
?
{{{a=a+(b-a)}}}
{{{0=b-a}}}
{{{b=a}}}
-
b=b-(a+b)
b=-a
One possibility is, a=0 and b=0.