Question

3．当t=$\frac{1}{8}$时，求$\frac{t+1}{{t}^{\frac{1}{3}}+1}$+$\frac{t-1}{{t}^{\frac{2}{3}}+{t}^{\frac{1}{3}}+1}$-$\frac{t-{t}^{\frac{1}{3}}}{{t}^{\frac{1}{3}}-1}$的值．

Answer 1

分析 利于已知条件求出${t}^{\frac{1}{3}}$的值，代入所求表达式，求解即可．

解答 解：t=$\frac{1}{8}$，
则${t}^{\frac{1}{3}}$=${（\frac{1}{8}）}^{\frac{1}{3}}$=$\frac{1}{2}$．
$\frac{t+1}{{t}^{\frac{1}{3}}+1}$+$\frac{t-1}{{t}^{\frac{2}{3}}+{t}^{\frac{1}{3}}+1}$-$\frac{t-{t}^{\frac{1}{3}}}{{t}^{\frac{1}{3}}-1}$=$\frac{\frac{1}{8}+1}{\frac{1}{2}+1}$+$\frac{\frac{1}{8}-1}{\frac{1}{4}+\frac{1}{2}+1}$-$\frac{\frac{1}{8}-\frac{1}{2}}{\frac{1}{2}-1}$
=$\frac{3}{4}$+$\frac{9}{14}$$-\frac{3}{4}$
=$\frac{9}{14}$．

点评 本题考查有理指数幂的运算考查计算能力．