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9.6 Adding and subtracting algebraic fractions

) Exercise 9.6

Throughout this exercise give each answer as a fraction in its simplest form.

1 Simplify these expressions.
x
x
a x + x b x + x 3 c x + d 2x − e 7x − x f 8x − 2x
5 5 7 7 8 8 3 3 15 15 9 9
g y + y h 2y + y i 2y + 3y j y − y k 2y − y l 4y − 5y
2 4 3 9 5 10 2 8 5 25 7 14
2 Copy and complete these calculations.

a aa a 5 + a W b bb b 3 + b W c 5c − 2c = 25c − c W
+=
+=
2 5 10 10 4 3 12 12 7 5 35 35
= 5a + aW = 3b + bW = 25c − cW
10 12 35
= Wa = Wb = Wc
10 12 35

d 5d + 3d = W d + W d e 5e + 2e = e W + e W f 9f + 3f = WW
+
6 5 30 30 8 3 24 24 10 4 20 20
+
+ We
+ Wd
= Wd 30 = We 24 = WW
20
= Wd = We = W
30 24 20
3 Simplify these expressions.
y
y
y
a x + b x + c 2x + d 2x − y e 11x − 2y f 9x − 2y
5 5 26 3 9 5 10 14 7 20 5
+
−
+
g ab h 2ab i 5a + 3b j ab k 3a − b l 4a − 3b
4 3 5 6 12 8 58 10 15 9 5
4 Here are some algebraic fraction cards.
The red cards are question cards. The blue cards are answer cards.
A 9x − 13x C 2x + 3x E 7x 5x F x + x i x
10 20 7 14 9 − 18 12 6 4

B x + x D 13x G x + x 3 ii x
6 3 11x − 36 30 10 2
18

a Which question cards match answer card i? Show your working.
b Which question cards match answer card ii? Show your working.
c Which question card does not match either of the answer cards?
Explain your answer.
d Explain how you can use normal fractions rather than algebraic fractions to work out the
answers to parts a, b and c.

9 Expressions and formulae 93