Merge pull request #1026 from iAngkur/patch-2

jakobkogler · web-flow · commit 115509c5a5ed · 2023-01-26T22:04:57.000+01:00
Update module-inverse.md
diff --git a/src/algebra/module-inverse.md b/src/algebra/module-inverse.md
@@ -120,7 +120,7 @@ Instead of computing the inverse for every number, we can expand the fraction by
 
 $$
 \begin{align}
-x_i^{-1} &= \frac{1}{x^i} = \frac{\overbrace{x_1 \cdot x_2 \cdots x_{i-1}}^{\text{prefix}_{i-1}} \cdot ~1~ \cdot \overbrace{x_{i+1} \cdot x_{i+2} \cdots x_n}^{\text{suffix}_{i+1}}}{x_1 \cdot x_2 \cdots x_{i-1} \cdot x_i \cdot x_{i+1} \cdot x_{i+2} \cdots x_n} \\
+x_i^{-1} &= \frac{1}{x_i} = \frac{\overbrace{x_1 \cdot x_2 \cdots x_{i-1}}^{\text{prefix}_{i-1}} \cdot ~1~ \cdot \overbrace{x_{i+1} \cdot x_{i+2} \cdots x_n}^{\text{suffix}_{i+1}}}{x_1 \cdot x_2 \cdots x_{i-1} \cdot x_i \cdot x_{i+1} \cdot x_{i+2} \cdots x_n} \\
 &= \text{prefix}_{i-1} \cdot \text{suffix}_{i+1} \cdot \left(x_1 \cdot x_2 \cdots x_n\right)^{-1}
 \end{align}
 $$
