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

b2-6b+9b2-b-6b2-94
Multiply the numerator by the reciprocal of the denominator.
b2-6b+9b2-b-6⋅1b2-94
Factor using the perfect square rule.
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
Factor b2-b-6 using the AC method.
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
Cancel the common factor of (b-3)2 and b-3.
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
Simplify the denominator.
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)