Page 28 - 新思维数学活动用书9 样章

2.5 Simplifying algebraic fractions

10 a Expand and simplify each expression.
i (a − 1)(a + 1)
ii (a − 4)(a + 4)
iii (a + 9)(a − 9)
b What do you notice about your answers in part a?

c Write the simplified expansion of (a − 8)(a + 8).
d Write the simplified expansion of (a + b)(a − b).

Challenge

11 Show that (x + 4)(x − 3) + x(5 − x) = 6(x − 2).
12 a Expand and simplify. i (x + 6) ii (x + 5)(x + 7) Tip
2
b What do you notice about your answers to part a, i and ii? In Question 11,
13 a Expand and simplify. i (x + 7) ii (x + 6)(x + 8) start by working
2
b What do you notice about your answers to part a, i and ii? with the left-
14 Try some examples of your own, similar to questions 12 and 13. hand side of the

What general rules do you notice? equation.
2
15 a Show that (2x + 1)(3x + 2) = 6x + 7x + 2.
b Expand and simplify.
i (3x + 1)(4x + 5) ii (4y + 3)(2y − 5)

2.5 Simplifying algebraic fractions

Exercise 2.5 Key word
Throughout this exercise, give each answer as a fraction in its algebraic fraction

simplest form.

Focus
1 Copy and complete these calculations.

3
1
a 1 += b 1 + 2 = c 2 +=
3 3 3 5 5 7 7
d 1 + 3 = 4 = e 1 + 2 = = f 3 + 3 = =
8 8 8 9 9 10 10

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