worksheet 2.1 algebraic fractions name: · © john wiley & sons australia, ltd page 1 worksheet...
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© John Wiley & Sons Australia, Ltd Page 1
WorkSHEET 2.1 Algebraic fractions Name: ___________________________ 1
If a = 21 and b = 5
2 , evaluate:
(a) 3a – 2b
(b) ab3
2
107
108
1015
54
23
522
213
23)a(
=
-=
-=
´-´=
- ba
758
32
254
23
25423254213
52
3)b(
2
2
=
´=
÷=
=
´
÷øö
çèæ
=
ab
© John Wiley & Sons Australia, Ltd Page 2
2 If 2
21 atuts += , evaluate s when:
(a) u = 0, a = 9.8 and t = 10 (b) u = –3, a = 10 and t = 5
490
108.921100
21)a(
2
2
=
´´+´=
+= atuts
2
2
1(b)213 5 10 52
110
s ut at= +
= - ´ + ´ ´
=
3 For each of the following, complete the relationship that illustrates the stated law. (a) Associative Law
(5x ´ 3y) ´ 2z = ___________________ (b) Commutative Law
8t + 7e = _______________________ (c) Commutative Law
8t ÷ 7e ¹ _______________________ (d) Identity Law
125h ´ 1 = _____________________ (e) Inverse Law
–3x + ___ = _____________________
(a) (5x ´ 3y) ´ 2z = 5x ´ (3y ´ 2z) (b) 8t + 7e = 7e + 8t (c) 8t ÷ 7e ¹ 7e ÷ 8t (d) 125h ´ 1 = 125h (e) −3x + 3x = +3x + −3x = 0
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4 Simplify the following expressions:
(a) 42
3 xx+
(b) 312
51 -+
+ aa
(a) 42
3 xx+
= 44
6 xx+
= 47x
(b) 312
51 -+
+ aa
= 15
)12(515
)1(3 -+
+ aa
= 15
51033 -++ aa
= 15213 -a
5 Simplify each of the following:
(a) xx 83
41+
(b) xx 81
52-
(a) xx 83
41+
= xx 83
82+
= x85
(b) xx 81
52-
= xx 405
4016
-
= x40
11
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6 Simplify the following by writing as a single fraction:
(a) 1
332
-+
+ xx
x
(b) 112
13
-+
-++
xx
xx
(a) 1
332
-+
+ xx
x
= )1)(3(
)1(2-+
-xx
x +)1)(3()3(3-+
+xx
xx
= )1)(3(9322 2
-+++-
xxxxx
= )1)(3(2113 2
-+-+
xxxx
(b) 112
13
-+
-++
xx
xx
= )1)(1()1)(12(
)1)(1()1)(3(
-+++
--+-+
xxxx
xxxx
= )1)(1(
)122(33 22
-++++--+-
xxxxxxxx
= )1)(1(
)132(32 22
-+++--+
xxxxxx
= )1)(1(
13232 22
-+----+
xxxxxx
= 2 4
( 1)( 1)x xx x- - -+ -
7 Simplify each of the following:
(a) y
x 306´
(b) yz
xy1415
521
´
(a) y
x 306´
= yx5
(b) yz
xy1415
521
´
= xz29
© John Wiley & Sons Australia, Ltd Page 5
8 Simplify each of the following:
(a) )5(2)7(
)3)(7()5(
++
´++
+xx
xxx
(b) 10
)14()14(
15 +´
-xx
xx
(a) )5(2)7(
)3)(7()5(
++
´++
+xx
xxx
= )3(2
1+x
(b) 10
)14()14(
15 +´
-xx
xx
= )14(2)14(3
-+xx
9 Simplify each of the following:
(a) xx46
÷
(b) xx 1021
27÷
(a) xx46
÷
= 4
6 xx´
= 23
(b) xx 1021
27÷
= 2110
27 xx´
= 35
10 Simplify each of the following:
(a) )1()3(
)5)(1()3(5
-+
÷-+
+xx
xxx
(b) )32(2)7(
)32)(7(18
--
÷-- x
xxx
(a) )1()3(
)5)(1()3(5
-+
÷-+
+xx
xxx
= )3()1(
)5)(1()3(5
+-
´-+
+xx
xxx
= )5)(1(
)1(5-+
-xx
x
(b) )32(2)7(
)32)(7(18
--
÷-- x
xxx
= )7()32(2
)32)(7(18
--
´-- x
xxx
= 2)7(
36-x