3u2-3u2-5u-6

Factor 3 out of 3u2-3.

Factor 3 out of 3u2.

3(u2)-3u2-5u-6

Factor 3 out of -3.

3(u2)+3(-1)u2-5u-6

Factor 3 out of 3(u2)+3(-1).

3(u2-1)u2-5u-6

3(u2-1)u2-5u-6

Rewrite 1 as 12.

3(u2-12)u2-5u-6

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.

3(u+1)(u-1)u2-5u-6

3(u+1)(u-1)u2-5u-6

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -6 and whose sum is -5.

-6,1

Write the factored form using these integers.

3(u+1)(u-1)(u-6)(u+1)

3(u+1)(u-1)(u-6)(u+1)

Cancel the common factor.

3(u+1)(u-1)(u-6)(u+1)

Rewrite the expression.

3(u-1)u-6

3(u-1)u-6

Simplify (3u^2-3)/(u^2-5u-6)