数学 - 整式の除法と分数式(積と商)

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数学読本〈1〉数・式の計算/方程式/不等式の第2章(文字と記号の活躍 - 式の計算)2.3(整式の除法と分数式)問20を解いてみる。

問20.

(1)

$\frac{x + 7}{x}$

(2)

$\frac{(x + y) {(x - y)}^{2}}{{(x - y)}^{2} \cdot x \cdot (x + y)} = \frac{1}{x}$

(3)

$\frac{(x + 1) (x + 2) (x + 4) (x - 3)}{(x - 2) (x - 3) (x + 1) (x + 3)}$

= $\frac{(x + 2) (x + 4)}{(x - 2) (x + 3)}$

(4)

$\frac{5 (x - 1) (x + 2) (x^{2} - 2 x + 4)}{(x - 6) (x + 2) \cdot 4 (x + 1) (x - 1)}$

= $\frac{5 (x^{2} - 2 x + 4)}{4 (x - 6) (x + 1)}$

(5)

$\frac{(a - 2) (a - 3) (2 a + 2) (3 a + 2)}{(a - 1) (3 a + 2) (a - 3) (a + 2)}$

= $\frac{2 (a - 2) (a + 1)}{(a - 1) (a + 2)}$

(6)

$\frac{1 - b}{a}$

(7)

$\frac{(2 x - 5) (3 x + 4) (x - 2) (x + 1) \cdot x \cdot (x + 2)}{(x + 2) (x - 2) \cdot 3 x \cdot (2 x - 5) (x + 1) (3 x + 4)}$

= $\frac{1}{3}$

(8)

$\frac{x^{2} + 4 x + 3}{(x - 1) (x - 3)} \cdot \frac{x^{2} - 4 x + 3}{(x + 1) (x + 3)} = 1$

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