The problem likely stems from the tag. Moreover, it does not seem to work well with hyperref, as a reference with \hyperref[fail:test_tag]{my text} online(!) seems to display the text associated with the label instead of the text in the \hyperref: see this description.
Conclusion: avoid \tag (or investigate and modify this text accordingly!).
\begin{align*} \important{\frac{a}{b} = \frac{c}{d}} &\iff \important{ad = bc} \tag *{equality of (numeric) fractions (cross-multiplication)}\label{fail:test_tag}\\ \\ \frac{a}{b}+\frac{c}{d} \quad &\perdef \quad \frac{ad+cb}{bd} \tag *{addition (common denominator)}\label{fail:optelling breuken} \\ \\ \frac{a}{b} \cdot \frac{c}{d} \quad &\perdef \quad \frac{a\cdot c}{b\cdot d} \tag *{multiplication (numerator $\times $ numerator, denominator $\times $ denominator) }\label{fail: vermenigvuldiging breuken} \\ \\ \frac{a}{b} : \frac{c}{d} \quad &\perdef \quad \frac ab \cdot \frac dc = \frac{a\cdot d}{b\cdot c} \tag *{division (multiply by the reciprocal)}\label{fail: deling breuken} \\ \end{align*}
With tabular (and center):
| x | 1 |
| y | 2 |
| z | 1 |
With tabular and @{} (and center):
| x | 1. |
| y | 2. |
| z | 1. |
With tabular and p{} (and center):
| x | 1 | 2 |
| y | 2 | 3 |
| z | 1 | 4 |
With array:
With array:
| The | domain | of a function is the set of all admissible inputs of the function. |
| The | image | of a function is the set of all actual outputs of the function. |