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--- exam_infos:preparation [2023/02/02 10:59] – [Do physics right] mexleadmin
+++ exam_infos:preparation [2023/02/02 13:28] (aktuell) – [Do math right] mexleadmin
@@ Zeile 3: / Zeile 3: @@
 ===== Do math right =====
-  * calculate fractions in fractions correct: \begin{align*} {{{A}\over{B}}\over{C}} \quad &\neq \quad {{A}\over{{B}\over{C}}} \\ {{{A}\over{B}}\over{C}} = {{A}\over{{B}\cdot{C}}} \quad &\neq \quad {{A}\over{{B}\over{C}}} = {{A\cdot C}\over{B}} \end{align*}
+  * calculate fractions in fractions (complex fractions) correct
+    * Be aware which is the longest fraction line: \\  \begin{align*} {{{A}\over{B}}\over{C}} \quad &\neq \quad {{A}\over{{B}\over{C}}} \\ {{{A}\over{B}}\over{C}} = {{A}\over{{B}\cdot{C}}} \quad &\neq \quad {{A}\over{{B}\over{C}}} = {{A\cdot C}\over{B}} \end{align*}
+    * Be aware how to reduce complex fractions by multiplying numerator and denominator with a factor: \\ \begin{align*} { { {{5 \cdot {{1}\over{x}} } \over {5 + {{1}\over{x}} } }  } \over { 7 + {{2}\over{x}} } } &\xrightarrow{either} &&{ { {{5 \cdot {{1}\over{x}} } \over {5 + {{1}\over{x}} } } \cdot \color{blue}{{| \cdot x}\over{| \cdot x}} } \over { 7 + {{2}\over{x}} } } && = { { {{5 } \over {5x + 1 } } } \over { 7 + {{2}\over{x}} } } \\ &\xrightarrow{\quad or \quad} &&{ { {{5 \cdot {{1}\over{x}} } \over {5 + {{1}\over{x}} } } } \over { 7 + {{2}\over{x}} } } \cdot \color{blue}{{| \cdot x}\over{| \cdot x}} = { { {{5 \cdot {{1}\over{x}} } \over {5 + {{1}\over{x}} } } \cdot \color{blue}{{| \cdot x}\over{ }} } \over { 7 + {{2}\over{x}} } } \cdot \color{blue}{{ }\over{| \cdot x}} && = { { {{5 } \over {5 + {{1}\over{x}} } } } \over { 7x + 2 } } \end{align*} \\ So please never never multiply in such cases all numerators and denominator with the factor...
   * Rearrange fractions correct: based on $\beta = {{I_C}\over{I_B}}$ on **cannot** derive $I_B = {{\beta}\over{I_C}}$..
 ===== Do physics right =====