当前位置:首页 > 八年级 > 数学试卷

【330005】15.1.2分式的基本性质(1)

时间:2025-02-07 09:17:04 作者: 字数:3011字

 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

15.1.2分式的基本性质(1

学习目标

  1. 能类比分数的基本性质,推出分式的基本性质。

2、理解并掌握分式的基本性质,能进行分式的等值变形。

学习重点:分式的基本性质及其应用。

学习难点:利用分式的基本性质,判断分式是否有意义。

课前预习

1小学里学过的分数的基本性质的内容是什么?

由分数的基本性质可知,如数c≠0,那么 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

2你能通过分数的基本性质猜想分式的基本性质吗?试一试归纳:分式的基本性质:

用式子表示为

3分解因式(1x2-2x = 23x2+3xy=

3a2-4= (4) a2-4ab+b2=

练习:

1p129的“例2”

2、填空:(1 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 、 (2 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

3、例2、下列分式的变形是否正确?为什么?

1 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>2 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>




4、不改变分式的值,使分式 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 的分子与分母各项的系数化为整数




5、 不改变分式的值,使下列分式的分子与分母都不含“—”号:

1 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 、 (2 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 、 (3 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

4)— <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>5 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>6)— <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>






课内探究

1、不改变分式的值,使下列分式的分子与分母都不含“—”号:

1 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> = 、(2)— <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> =

2、填空:(1 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> = <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 2 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 、(3 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

3、若把分式 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 中的xy都扩大3倍,那么分式的值是

4、不改变分式的值,使下列分式的分子与分母的最高次项的系数化为正数。

1 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>2 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>3 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

5、 下面两位同学做的两种变形,请你判断正误,并说明理由.

甲生: <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> ;

乙生: <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>




课后训练

1、下列各式中,整式有 ,分式有 。(填序号)

 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

2、写出一含有字母x的分式_______

3、当 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 取什么值时,下列分式有意义:(提示:要使分式有意义,则分母 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 0

1 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 解: ∵  <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 0,∴

2 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 解: ∵  <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 0,∴

3 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 解: ∵  <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 0,∴

4 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 解: ∵  <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 0,∴

4、当x为何值时,分式值为零?(提示:分式的值为零,分子=0,且分母 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a> 0

1 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>2 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>








5、根据分式的基本性质填空:

1 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>  <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>2 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

3 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>4 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>  <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

6、不改变分式的值,使下列分式的分子与分母都不含“-”号。

1 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>2 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>3 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>

4 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>5 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>6 <a href="/tags/253/" title="基本" class="c1" target="_blank">基本</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/846/" title="分式" class="c1" target="_blank">分式</a>