学习了有理数的乘除后，李老师给何平平出了一道题：有两个数-4和6，它们的倒数积为x，它们的倒数和为y，它们和的倒数为z，求$x\div y\cdot z$的值。你能帮助何平平解决这个问题吗？

能.

依题意得：

$x=-\dfrac {1} {4}\times \dfrac {1} {6}=-\dfrac {1} {24}$

$y=-\dfrac {1} {4}+\dfrac {1} {6}=-\dfrac {1} {12}$

$z=\dfrac {1} {-4+6}=\dfrac {1} {2}$

$\therefore x\div y\cdot z$

$=\left ( {-\dfrac {1} {24}} \right )\div \left ( {-\dfrac {1} {12}} \right )\times \dfrac {1} {2}$

$=\dfrac {1} {24}\times 12\times \dfrac {1} {2}$

$=\dfrac {1} {4}$