[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