1992 年

$\dfrac{1}{a}+\dfrac{1}{b}=$

If $a=1-\dfrac{1}{1-b}$, then $b=$

For what value(s) of $x$ does the equality $\dfrac{(x+1)(x-2)}{x-2}=x+1$ hold?

$\dfrac{\sqrt5+1}{\sqrt5-1}-\dfrac{\sqrt5-1}{\sqrt5+1}=$

If $\log_{10}b=1+\dfrac{1}{2}\log_{10}a$, then $b=$

Which of the following is a factor of $4(a+b)^2-9(a-b)^2$?

If $\dfrac{a}{b}=\dfrac{c}{d}=k$ and $a,b,c,d$ are positive, then which of the following must be true?

Simplify $\dfrac{\overbrace{n\times n\times\cdots\times n}^{n\text{ times}}}{\underbrace{n+n+\cdots+n}_{n\text{ terms}}}$.

If $a$ and $b$ are greater than 1, which of the following statements is/are true? I. $\sqrt{a+b}=\sqrt{a}+\sqrt{b}$ II. $(a^{-1}+b^{-1})^{-1}=a+b$ III. $a^2b^3=(ab)^6$

If $a:b=2:3$, $a:c=3:4$ and $b:d=5:2$, find $c:d$.