Math topic中文

Multiply divide fractions

multiplication and division of simple algebraic fractions such as: $\left(\dfrac{3a}{4b^{2}}\right)\left(\dfrac{5ab}{3}\right)$ ; $\quad \dfrac{3a}{4} \div \dfrac{9a^{2}}{10}$

Practice questions

1先化简，再求值： $( \dfrac {x}{x-2}- \dfrac {x}{x+2})÷ \dfrac {4x}{x-2}$ ，其中 $x=2016$ ．
2 $\displaystyle \frac{2x^2-5xy-12y^2}{x^2-16y^2}$ Simplify. Answer ...
3先化简，再求值： $\frac { x ^ { 2 } -2x+1 } { x ^ { 2 } +3x }÷\left ( { 1-\frac { 4 } { x+3 } } \right )$ ，然后从 $-3$ ，0，1，3中选…
4Write $9^{2x+1}$ as a power of 3. Simplify $\dfrac{9a^2}{4b}\left(\dfrac{27a^3b}{6}\right)^{-1}$ .
5化简 $\left(a+\dfrac{3a-4}{a-3}\right)\left(\dfrac{1}{a-2}-1\right)$ 的结果等于 $(\quad).$ A. $-a-2$ B. $\dfrac{a-2}{a-3}$ …
6Solve the equation $\displaystyle \frac{3-2x}{7} = \frac{1}{3}(2x-1).$ Answer x = ... Simplify $\displaystyle \frac{25a^{2}-9b^{2}}{15a-10ab+6b^{2}-9b}$ …
7Express $x^2-6x-2$ in the form $(x-a)^2 + b$ where $a$ and $b$ are constants. Answer ___ Hence, state the minimum value…
8Write as a single fraction in its simplest form. $\dfrac{3t^2}{w} \cdot \dfrac{9t^2}{w^3}$ Answer ----------------------…
9计算： $(1) \dfrac {1}{x-3}- \dfrac {1}{3+x}(2)m-1+ \dfrac {2m-6}{m^{2}-9}÷ \dfrac {2m+2}{m+3}$ ．
10化简 $\dfrac {2}{x^{2}-4}- \dfrac {1}{2x-4}$ ．
11先化简，再求值： $\dfrac{x}{{x}^{2}-2x+1}÷( \dfrac{x+1}{{x}^{2}-1}+1)$ ，其中 $x= \sqrt{2}+1 .$
12Simplify $\displaystyle\frac{16a^6 b^2}{5} - \displaystyle\frac{8a^3}{25ab^3}$ . Answer ___ (i) Express $-4x + x^2 - 6$ i…
13先化简，再求值 $( \dfrac {x^{2}-3}{x-1}-2)÷ \dfrac {1}{x-1}$ ，其中 $x$ 满足 $x^{2}-2x-3=0$ ．
14Given that $\cos(A+B)= -\dfrac{5}{13}$ and $\sin A\sin B=\dfrac{15}{26}$ , where A and B are acute angles and angle A > a…
15Simplify $\left(\dfrac{a^6 b^3}{8}\right)^{\tfrac{1}{3}}\times\dfrac{3b^{-1}}{a^2}$ . Answer ... Solve $\dfrac{2}{x-2}+\dfrac{3}{x+2}=0$ …
16Factorise $\dfrac{6a-15a^2+20ab-8b}{25a^3-4a}$ completely.
17计算： $(1)(1+\dfrac{1}{x})\cdot \dfrac{x}{{{x}^{2}}-1}(2)\dfrac{2{{x}^{2}}+{{y}^{2}}}{x+y}-\dfrac{{{x}^{2}}+2{{y}^{2}}}{x+y}$ …
18若 $\dfrac {x}{y}=3$ ，求 $(1+ \dfrac {y^{2}}{x^{2}-y^{2}})÷ \dfrac {x}{x-y}$ 的值．
19Simplify $\left(\dfrac{-2p^{3}}{q^{-1}}\right)^{2}\div\left(\dfrac{8q^{4}}{p^{3}}\right)^{\tfrac{1}{3}}$ , giving your an…
20计算： $(1) \dfrac {x^{2}}{x-5}+ \dfrac {25}{5-x}(2) \dfrac {1}{x-1}- \dfrac {x}{x^{2}-1}(3) \dfrac {x+2}{x^{2}-2x}- \dfrac {x-1}{x^{2}-4x+4}(4) \dfrac {a}{a+1}+ \dfrac {a-1}{a^{2}-1}(5) \dfrac {x^{2}}{x-1}-x-1(6) \dfrac {x^{2}-1}{x^{2}-2x+1}⋅ \dfrac {x-1}{x^{2}+x}$ …
21Simplify $\dfrac{9x^2 - 4}{12x^2 - x - 6}$ . Answer ...
22ABCD is a parallelogram and triangle CDE is isosceles. E and F are points on AD and BC respectively. AB, EF and CD are p…
23Given that $a = \sqrt{\frac{b^2+4ac}{2a}}$ , find the values of $b$ when $a = 4$ and $c = -1$ . Answer b = ... Simplify $\left(\dfrac{125p^6}{q^3}\right)^{-1/3}\times\left(\dfrac{3p^0}{\sqrt{q}}\right)^2$ …
24Express $\frac{12xy^2}{15} \div \frac{2xy^3}{(3x)^2}$ as a single fraction in its simplest form. Given that $\dfrac{v}{3} = \sqrt[3]{\dfrac{2s+v}{s-3}}$ …
25先化简，再求值 $1- \dfrac {a-2}{a}÷ \dfrac {a^{2}-4}{a^{2}+a}$ ，请你找一个合适的 $a$ 的值代入求值．
26解下列各题 (1)先化简： $(2x- \dfrac {x^{2}+1}{x})÷ \dfrac {x^{2}-2x+1}{x}$ ，然后从 $0$ ， $1$ ， $-2$ 中选择一个适当的数作为 $x$ 的值代入求值． (2)解方程： $\dfrac {3}{x+1}= \dfrac {x}{x-1}-1$ …
27先化简再求值： $( \dfrac {3}{x-1}-x-1)÷ \dfrac {x-2}{x^{2}-2x+1}$ ，其中 $x$ 是方程 $x^{2}=2x$ 的根．
28判断代数式 $(\dfrac{2{{a}^{2}}+2a}{{{a}^{2}}-1}-\dfrac{{{a}^{2}}-a}{{{a}^{2}}-2a+1})\div \dfrac{a}{a+1}$ 的值能否等于 $-1$ ？并说明理由．
29化简求值： $⑴\left(1+x+ \dfrac{{x}^{2}}{1-x}\right)÷ \dfrac{1+x}{1-x},x=-3 ⑵\left( \dfrac{x+2}{{x}^{2}-2x}- \dfrac{x-1}{{x}^{2}-4x+4}\right)÷ \dfrac{x-4}{x},x=-5$ …
30Write $\frac{2}{x-2} - \frac{3}{2x+1}$ as a single fraction in its simplest form. Answer ...
31下列计算正确的是 $(\quad)$ A. $a^{3}\boldsymbol{⋅}(-a)^{2}=a^{5}$ B. $(3a^{3}b)^{2}=3a^{6}b^{2}$ C. $a^{-5}÷a^{2}=a^{-3}$ …
32如果把 $\dfrac{x+y}{5xy}$ 中的 $x$ 与 $y$ 都扩大为原来的 $5$ 倍，那么这个代数式的值 $(\quad)$ A. 不变 B. 扩大为原来的 $5$ 倍 C. 缩小为原来的 $\dfrac{1}{5}$ D…
33(1)解方程： $x^{2}-5x+3=0(2)$ 计算： $(\dfrac{3}{x+2}+x-2)÷\dfrac{x^{2}-2x+1}{x+2}$
34(1)解不等式组并把它的解集在数轴上表示出来． $\begin{cases}4x\leqslant 2(x+3) \\ \dfrac{1}{2}x-1 > - \dfrac{3}{2}x\end{cases} (2)$ 先化简，再求值： ${{\left( \dfrac{2a{{b}^{2}}}{a+b} \right)}^{3}}\div {{\left( \dfrac{a{{b}^{3}}}{{{a}^{2}}-{{b}^{2}}} \right)}^{2}}\cdot {{\left[ \dfrac{1}{2(a-b)} \right]}^{2}}$ …
35Simplify $\displaystyle \frac{a^2-3a+2}{9a^2-1}\;\div\;\frac{2a-2}{6a-2}$ Answer: ...
36(1)计算： $\sqrt[3]{8}-(π-3)^{0}+( \dfrac {1}{2})^{-1}+| \sqrt {2}-1|$ ． (2)化简： $( \dfrac {x^{2}}{x-2}- \dfrac {4}{x-2})⋅ \dfrac {1}{x^{2}+2x}$ …
37先化简，再求值： $\dfrac {x^{2}+2x+1}{x+2}÷ \dfrac {x^{2}-1}{x-1}- \dfrac {x}{x+2}$ ，其中 $x= \sqrt {3}-2$ ．
38已知：长方形的面积为3xy+6y，宽为3y，则长方形的长是．
39先化简，再求值： $(1+ \dfrac {1}{x-2})÷ \dfrac {x^{2}-2x+1}{x-2}$ ，其中 $x=4-\tan 45^{\circ}$ ．
40先化简，再求值： $1-\dfrac{a-2}{a}÷\dfrac{a^{2}-4}{a^{2}+a}$ ，从 $-2$ ， $-1$ ， $0$ ， $1$ ， $2$ 中选择一个合适的数代入，此分式的值可能是 $(\quad)$ A.…
41(1)计算： $( \dfrac {1}{2})^{-3}+| \sqrt {3}-2|-(-2017)^{0}$ ． (2)先化简，再求值：已知： $( \dfrac {1}{x-2}+1)÷(x+ \dfrac {1}{x-2})$ ，…
42下列结论：①不论 $a$ 为何值 $\dfrac{a}{{a}^{2}+1}$ 都有意义；② $a=-1$ 时，分式 $\dfrac{a+1}{{a}^{2}-1}$ 的值为 $0$ ；③若 $\dfrac{{x}^{2}+1}{x-1}$ …
43Simplify (i) $\dfrac{1}{\sqrt[a]{x}}\times b + \left(\dfrac{2}{ab}\right)^{-2}$ . Answer ___ (ii) $\dfrac{4x^2-36}{2x^2-20x+42}$ …
44先化简 $\dfrac {x^{2}-1}{x}÷(x- \dfrac {2x-1}{x})$ ，再任选一个适当的整数代入求值．
45Simplify $\frac{5a^3}{6b} + \frac{2ab}{4a^2b}$ . Solve $\frac{x}{8} = \frac{50}{x}$ . Simplify $\frac{4v^2 - 1}{2pv + p - 10v - 5}$ …