讲解这几道题---Extraction Content:
Title: 追梦专项一 大题抢分练 (Dream Chasing Special Topic 1 - Big Problems Score Grabbing Practice)
Knowledge Point 1: 因式分解、分式(方程)及不等式(组)的相关计算 (Related Calculations of Factoring, Rational Expressions (Equations), and Inequalities (Systems))
Problem 1:
Points: 8 分 (8 points)
Question Stem: 因式分解. (Factorize.)
(1) 3a³-6a²b+3ab²
(2) 2. 2² +4. 4×17. 8+17. 8² (Note: This might be intended as 2.2^2 + 2 * 2.2 * 17.8 + 17.8^2 or similar variations, interpreting "4. 4" as "4.4" and assuming a structure for factoring or calculation).
Problem 2:
Points: 8 分 (8 points)
Question Stem: 解方程. (Solve the equation.)
(1) 2x/(x-2) + 1 = 5/(2-x)
(2) 2x/(x+3) + 1 = 7/(2x+6)
Problem 3:
Points: 8 分 (8 points)
Question Stem: 先化简, 再求值: (2a+1)/(a²-1) * (a²-2a+1)/(a²-a) - 1/(a+1), 从 -1 ≤ a ≤ 2 的整 数中选取一个你认为合适的 a 的值, 代入求值. (First simplify, then evaluate: (2a+1)/(a²-1) * (a²-2a+1)/(a²-a) - 1/(a+1), choose a suitable integer value for a from -1 ≤ a ≤ 2 and substitute to find the value.)
Problem 4:
Points: 8 分 (8 points)
Question Stem: 解不等式组: [ x-3(x-2) ≥ -2, (2x-1)/3 > (x-1)/2 ], 并把它的解集在数轴上表示出来. (Solve the system of inequalities: [ x-3(x-2) ≥ -2, (2x-1)/3 > (x-1)/2 ], and represent its solution set on the number line.)
Chart Description:
Type: Number line diagram.
Main Elements:
- A horizontal line with arrows on both ends indicating it extends infinitely.
- Tick marks are present at integer values from -4 to 5.
- Labels are present at each tick mark: -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.
Left Margin Notes:
注意事项: (Notes:)
① 请写好学校、班级、姓名、考号。 (① Please write your school, class, name, and exam number properly.)
② 请看清题目后再仔细做题。 (② Please read the questions clearly before doing them carefully.)
③ 要求书写工整, 字迹清晰, 卷面整洁。 (③ Requires neat writing, clear handwriting, and a clean paper.)
封线内不要答题 (Do not write inside the sealed line) (This label indicates an area not to be used for answers, likely near a fold or binding line).