Page 30 - 新思维数学活动用书9 样章

2.5 Simplifying algebraic fractions

7 Simplify each expression.
a x + y b x + y c 3x + y
2 2 3 6 4 12

d 5x − y e 7x − 2y f 3a + b
6 18 12 3 4 7
g 5a + 5b h a − 5 i 2a − 5
9 6 7 b 9 4b
8 This is part of Seren’s homework.

Question

Simplify 8x + 2
2
Answer
8x + 2 8x + 2 = 8x
=
2 2

a Substitute x = 4 into 8x + 2 and work out the answer.
2
b Substitute x = 4 into 8x and work out the answer.
c Use your answers to parts a and b to show that Seren’s answer is incorrect. Explain the
mistake she has made.

d Copy and complete the correct solution for Seren.
2( x + 1) 2 ( x + 1)
1
8x + 2 = = = x + 1
2 2 2 1

9 Simplify these expressions. Make sure you factorise the numerator before you cancel with the
denominator.

a 10x + 5 b 15x + 3 c 12x − 16 d 18x − 24
5 3 4 6

Challenge

10 Evan thinks the expression 7x − 14 + 8x + 6 simplifies to 5x + 1.
7 2
Is Evan correct? Show your working.

11 a Show that the fraction 8x + 24 can be simplified to 2x + 6 or 2(x + 3).
4
b Simplify these fractions. Write two expressions for each answer; one with brackets and one
without brackets.

−
i 6x + 12 ii 15x + 45 iii 24x − 36 iv 32 48x
3 5 4 8

29