[division of rational expressions][section 54]

(1.) 4a - 16
_______ (3a - 12) here is the problem
3a

= 4a - 16 1 multiply by the reciprocal
__________ * __________
3a 3a - 12

= 4(a - 4) 1
________ * ___________
3a 3(a - 4) factor

= 4
____ cancel and multiply
9a

(2.) 6z - 27
_______ (4z - 18) here is the problem
4z

= 3(2z - 9)
____________ 2(2z - 9) factor
4z

= 3(2z - 9) 1
____________ * __________ multiply by the reciprocal
4z 2(2z - 9)

= 3
_____ cancel and multiply
8z

(3.) (2x)3 16x2
_________ _______ here is the problem
(4xy)3 8y2z3

= (2x)3 8y2z3
__________ * __________ multiply by the reciprocal
(4xy)3 16x2

= 8x3 8y2z3
_________ * __________ cube 2 & 4 & multiply exponents
64x3y3 16x2

64x3y2z3

= _______________ multiply, add exponents
1024x5y3


= z3
______________ reduce, subtract exponents
16x2y


(4.) a2 - b2 a + b
________ __________
x2 - y2 x - y here is the problem

= (a - b)(a + b) (x - y) factor and multiply
__________________ * _________ by the reciprocal
(x - y)(x + y) (a + b)

= a - b
_____
x + y cancel and multiply

(5.) x - y 5x2 - 5y2
_____ __________ here is the problem
x + y 3x - 3y

= (x - y) 5(x2 - y2)
___________ ____________
(x + y) 3(x - y) factor

= (x - y) 5(x - y)(x + y)
_________ _________________
(x + y) 3(x - y) factor

= (x - y) 3(x - y) multiply by the
___________ * _______________ reciprocal
(x + y) 5(x - y)(x + y)

= 3(x - y)
___________
5(x + y) cancel and multiply

(6.) x2 + 2x + 1
______________ (x + 1) here is the problem
3x

= (x + 1)2 1 factor and multiply
___________ * __________ by the reciprocal
3x (x + y)

= (x + 1)
___________
3x cancel and multiply





(7.) a3 - 6a2 + 8a 2a - 4
______________ ____________ here is the problem
5a 10a - 40

= a(a - 4)(a - 2) 10(a - 4) factor and multiply
___________________ * ____________ by the reciprocal
5a 2(a - 2)

= (a - 4)2 cancel and multiply


(8.) k 1
_______________ ___________
k2 - 6k + 9 k - 3


= k (k - 3) factor and multiply
_________________ * ____________ by the reciprocal
(k - 3)2
1

= k/(k - 3) cancel and multiply



(9.) a2 - 49 3a - 21
___________ _____________ here is the problem
(a + 7)2 2a + 14

= (a - 7)(a + 7) 2(a + 7) factor and multiply
__________________ * _____________ by the reciprocal
(a + 7)2 3(a - 7)

= 2/3 cancel and multiply

(10.) b2 + 8b + 15
(b2 - 9) ______________ here is the problem
2b + 10

= (b - 3)(b + 3) 2(b + 5) factor and multiply
_________________ * ________________ by the reciprocal
1 (b + 5)(b + 3)

= 2(b - 3) cancel and multiply