==== 13. Februar 2017 bis 18. Februar 2017 ====
=== Dienstag 14. Februar 2017 ===
Vereinfachen Sie:
  - $$\left(x^{\frac{8}{3}}\right)^{\frac{13}{16}}: x^{\frac{3}{2}}$$
  - $$\left(x^{-\frac{3}{5}}\right)^{-\frac{115}{18}}: x^{\frac{3}{2}}$$
  - $$\left(x^{\frac{6}{5}}\right)^{\frac{1}{9}}\cdot x^{\frac{5}{3}}$$

<hidden Lösungen>
  - $$x^{\frac{2}{3}}$$
  - $$x^{\frac{7}{3}}$$
  - $$x^{\frac{9}{5}}$$
</hidden>


=== Donnerstag 16. Februar 2017 ===
Lösen Sie durch faktorisieren:
  - $x^2+4x+4 = 9$
  - $x^2-6x+9 = 4$
  - $x^2+8x+16 = 1$

<hidden Lösungen>
  - $(x+2)^2 = 9$ also $(x+2)=\pm 3$, also $x_{1}=-5$, $x_=1$.
  - $(x-3)^2 = 4$ also $(x-3)=\pm 2$, also $x_1=1$, $x_2=5$.
  - $(x+4)^2 = 1$ also $(x+4)=\pm 1$, also $x_1=-5$, $x_2=3$.
</hidden>
=== Freitag 17. Februar 2017 ===
Lösen Sie schrittweise auf:
  - $${{15x}\over{8}}+{{4}\over{3}}={{7x}\over{4}}+{{13}\over{8}}$$
  - $${{19x}\over{20}}+{{6}\over{5}}={{4x}\over{5}}+{{7}\over{5}}$$
  - $${{53x}\over{18}}+{{7}\over{6}}={{8x}\over{3}}+{{4}\over{3}}$$


<hidden Lösungen>
1.

$\begin{align*}
{{15x}\over{8}}+{{4}\over{3}} &= {{7x}\over{4}}+{{13}\over{8}} && |\cdot 24\\
45x+32 &= 42x+39 && |-\left(42x+32\right)\\
3x &= 7 && |:3\\
x &= {{7}\over{3}}
\end{align*}$

2.

$\begin{align*}
{{19x}\over{20}}+{{6}\over{5}} &= {{4x}\over{5}}+{{7}\over{5}} && |\cdot 20\\
19x+24 &= 16x+28 && |-\left(16x+24\right)\\
3x &= 4 && |:3\\
x &= {{4}\over{3}}
\end{align*}$

3.

$\begin{align*}
{{53x}\over{18}}+{{7}\over{6}} &= {{8x}\over{3}}+{{4}\over{3}} && |\cdot 18\\
53x+21 &= 48x+24 && |-\left(48x+21\right)\\
5x &= 3 && |:5\\
x &= {{3}\over{5}}
\end{align*}$

</hidden>