Page 46 - 新思维数学学生用书9 样章

2.5 Simplifying algebraic fractions

Continued

a Substitute x = 3 into 6x + 2 and work out the answer.
2
b Substitute x = 3 into 3x + 1 and work out the answer.

c Use your answers to parts a and b to show that Iain’s answer is correct.
d Look back at Iain’s solution and explain why his method works.
e Read what Arun says:

I use a much easier
method, I just cancel the
numbers that are the

same 6x + 1 2 = 6x + 1
1
2

Show that when x = 3, Arun’s answer is incorrect.
Explain why his method is incorrect.
f Discuss your answers to parts a to e with other learners in your class.

How will you convince them about your findings if your answers are
different?

8 Simplify these expressions. Make sure you factorise the Tip

numerator before you cancel with the denominator. In Question 9,
a 6x + 3 b 5x + 10 c 6x − 9 d 8x − 20 simplify each
3 5 3 4
9 Show that 6x − 4 + 20x + 25 simplifies to 7x + 3. fraction separately,
2 5 then add the
10 This is how Shania and Taylor simplify the fraction 6x + 18 . answers together.
3

Shania Taylor
Fully factorise 6x + 18 = 6(x + 3) The denominator is 3, so take out a
6x + 18 6(x + 3) factor of 3: 6x + 18 = 3(2x + 6)
3 = 3 6x + 18 3(2x + 6)
2 6(x + 3) 3 = 3
= 1 3 1 3(2x + 6)

= 2(x + 3) = 1 3
= 2x + 6

a Show that Shania’s answer is equivalent to Taylor’s answer.
b Critique both methods. Whose method do you prefer, Shania’s or Taylor’s? Explain why.

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