Question:
If $x / y$ is the additive inverse of $c / d$, then, $(x / y)-(c / d)=0$
Solution:
False.
Let $x / y=2 / 3$ and its additive inverse $c / d=-2 / 3$
Then, $(x / y)-(c / d)$
$=(2 / 3)-(-2 / 3)$
$=(2 / 3)+(2 / 3)$
$=4 / 3$
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