Further algebra
P3 7
EXERCISE 7B
Simplify the expressions in questions 1 to 10. 1
3
5
2
5xy 3
x2 − 9 − 9x + 18
4
5x − 1 × x 2 + 6x + 9 x + 3 5x 2 + 4x − 1
4x 2 − 25 + 20x + 25
6
a 2 + a − 12 × 3 5 4a − 12
8
2p + 4 ÷ (p 2 − 4) 5
6a b x2
a 9b 2
4x 2
7
4x 2 − 9 ÷ 2x − 3 x 2 + 2x + 1 x 2 + x
9
a2 − b2 2a 2 + ab − b 2
10
15xy 2
x 2 + 8x + 16 × x 2 + 2x − 3 x 2 + 6x + 9 x 2 + 4x
In questions 11 to 24 write each of the expressions as a single fraction in its simplest form. 11
1 4x
1 5x
12
x − (x + 1) 3 4
13
a + 1 a +1 a −1
14
2 + 3 x−3 x−2
15
x2
x − 1 −4 x+2
16
17
2 − a a + 1 a2 + 1
19
x
21
2 3 + 3(x − 1) 2(x + 1)
22
23
2 − a−2 a + 2 2a 2 + a − 6
24
1 x
1
p2 p2 − 2 −1 p +1
p2
18
2y − 4 (y + 2)2 y + 4
20
2 − 3 b 2 + 2b + 1 b + 1 6 5(x
2) (x
2x 2)2
1 +1+ 1 x−2 x x+2
Partial fractions Sometimes, it is easier to deal with two or three simple separate fractions than it is to handle one more complicated one. For example: 1 (1 2x)(1 x) may be written as 2 – 1 . (1 2x) (1 x) 166