u+3u2-1

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)