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3. 若$a = 2b\neq0$,则$\frac{4b^{2} - a^{2}}{a^{2} - ab} =$ .
答案
0
4. 判断下列约分是否正确,如果正确,在括号内打“√”；如果不正确,把正确答案写在括号内.
(1)$\frac{ax^{4}}{ax^{8}} = \frac{1}{x^{2}}$;( ) (2)$\frac{(-a - b)^{2}}{a + b} = -a - b$;( )
(3)$\frac{(x + 2)(x - 5)}{(2 + x)(5 - x)} = -1$;( )(4)$\frac{(x + y) + (x - y)}{2(x + y)(x - y)} = \frac{1}{2}$.( )
(1)$\frac{ax^{4}}{ax^{8}} = \frac{1}{x^{2}}$;( ) (2)$\frac{(-a - b)^{2}}{a + b} = -a - b$;( )
(3)$\frac{(x + 2)(x - 5)}{(2 + x)(5 - x)} = -1$;( )(4)$\frac{(x + y) + (x - y)}{2(x + y)(x - y)} = \frac{1}{2}$.( )
答案
(1)$\frac{1}{x^{4}}$ (2)a+b (3)√ (4)$\frac{x}{(x+y)(x−y)}$
5. 约分:
(1)$\frac{2ax^{2}y}{3axy^{2}}$; (2)$\frac{-2a(a + b)}{3b(a + b)}$; (3)$\frac{x^{2} - 4}{xy + 2y}$;
(4)$\frac{(a - x)^{2}}{(x - a)^{3}}$; (5)$\frac{a^{2} - 4a + 4}{a^{2} - 4}$.
(1)$\frac{2ax^{2}y}{3axy^{2}}$; (2)$\frac{-2a(a + b)}{3b(a + b)}$; (3)$\frac{x^{2} - 4}{xy + 2y}$;
(4)$\frac{(a - x)^{2}}{(x - a)^{3}}$; (5)$\frac{a^{2} - 4a + 4}{a^{2} - 4}$.
答案
(1)$\frac{2x}{3y}$ (2)$-\frac{2a}{3b}$ (3)$\frac{x−2}{y}$ (4)$\frac{1}{x−a}$ (5)$\frac{a−2}{a+2}$
1. 分式$\frac{12c}{4a}$、$\frac{a^{2} + b^{2}}{3(a + b)}$、$\frac{4a^{2} - b^{2}}{2a - b}$、$\frac{a - b}{b - a}$中,最简分式有 ( )
A. 1个 B. 2个 C. 3个 D. 4个
A. 1个 B. 2个 C. 3个 D. 4个
答案
A
2. 约分:
(1)$\frac{-12xy^{2}z^{3}}{6yz^{2}}$; (2)$\frac{4y^{2} - x^{2}}{-x^{2} + 4xy - 4y^{2}}$;
(3)$\frac{(1 - x)^{2}(1 + x)^{2}}{(x^{2} - 1)^{2}}$.
(1)$\frac{-12xy^{2}z^{3}}{6yz^{2}}$; (2)$\frac{4y^{2} - x^{2}}{-x^{2} + 4xy - 4y^{2}}$;
(3)$\frac{(1 - x)^{2}(1 + x)^{2}}{(x^{2} - 1)^{2}}$.
答案
(1)−2xyz (2)$\frac{x + 2y}{x - 2y}$ (3)1
3. 先化简，再求值:$\frac{(a + b)^{2} - 8(a + b) + 16}{(a + b)^{2} - 16}$,其中$a + b = 5$.
答案
$\frac{a+b−4}{a+b+4}$,$\frac{1}{9}$
