Divide (u+3)/(u^2-1)

u+3u2-1
Simplify the denominator.
Rewrite 1 as 12.
u+3u2-12
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=u and b=1.
u+3(u+1)(u-1)
u+3(u+1)(u-1)
Split the fraction u+3(u+1)(u-1) into two fractions.
u(u+1)(u-1)+3(u+1)(u-1)
Divide (u+3)/(u^2-1)