b2-6b+9b2-b-6b2-94

Multiply the numerator by the reciprocal of the denominator.

b2-6b+9b2-b-6⋅1b2-94

Rewrite 9 as 32.

b2-6b+32b2-b-6⋅1b2-94

Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.

2ab=2⋅b⋅-3

Simplify.

2ab=-6b

Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=b and b=-3.

(b-3)2b2-b-6⋅1b2-94

(b-3)2b2-b-6⋅1b2-94

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 -1.

-3,2

Write the factored form using these integers.

(b-3)2(b-3)(b+2)⋅1b2-94

(b-3)2(b-3)(b+2)⋅1b2-94

Factor b-3 out of (b-3)2.

(b-3)(b-3)(b-3)(b+2)⋅1b2-94

Cancel the common factors.

Cancel the common factor.

(b-3)(b-3)(b-3)(b+2)⋅1b2-94

Rewrite the expression.

b-3b+2⋅1b2-94

b-3b+2⋅1b2-94

b-3b+2⋅1b2-94

To write b2 as a fraction with a common denominator, multiply by 44.

b-3b+2⋅1b2⋅44-94

Combine b2 and 44.

b-3b+2⋅1b2⋅44-94

Combine the numerators over the common denominator.

b-3b+2⋅1b2⋅4-94

Rewrite b2⋅4-94 in a factored form.

Rewrite b2⋅4 as (b⋅2)2.

b-3b+2⋅1(b⋅2)2-94

Rewrite 9 as 32.

b-3b+2⋅1(b⋅2)2-324

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=b⋅2 and b=3.

b-3b+2⋅1(b⋅2+3)(b⋅2-3)4

Simplify.

Move 2 to the left of b.

b-3b+2⋅1(2⋅b+3)(b⋅2-3)4

Move 2 to the left of b.

b-3b+2⋅1(2b+3)(2b-3)4

b-3b+2⋅1(2b+3)(2b-3)4

b-3b+2⋅1(2b+3)(2b-3)4

b-3b+2⋅1(2b+3)(2b-3)4

Multiply the numerator by the reciprocal of the denominator.

b-3b+2(14(2b+3)(2b-3))

Multiply 4(2b+3)(2b-3) by 1.

b-3b+2⋅4(2b+3)(2b-3)

Multiply b-3b+2 and 4(2b+3)(2b-3).

(b-3)⋅4(b+2)((2b+3)(2b-3))

Move 4 to the left of b-3.

4(b-3)(b+2)(2b+3)(2b-3)

Simplify ((b^2-6b+9)/(b^2-b-6))/(b^2-9/4)