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Dresden Database Research Group 11

(e^{i*\pi*4/3})^{19} = e^{i*\pi*4/3*19}

\frac{2 / 3}{1/7}\cdot 1 = 2/3\cdot \frac11\cdot 7

\dfrac{y}{y^4} \cdot 28/70 = \frac{28 \cdot y}{70 \cdot y^4}

\sqrt{x} = x^{\frac12} = x^{3/6}

3 = \frac22\cdot 3

\pi\cdot 92/3 - \pi\cdot 30 = \frac{2}{3}\cdot \pi

\frac{1}{6^5} \cdot 651 = 651/7776 = 217/2592

1 + x^2 - 2*x = 1 + x^2 - 2*x

1/(f*d) = 1/(d*f) = \frac{1}{f*d}

5*\left(-1\right) - 17 = -22

\overline{u\times v} = |u\times v|^2/(u\times v) = |u|^2/u\times |v|^2/v

-\frac{1}{l + 1} + 1 = \frac{l}{l + 1}

\left(0 = 20\cdot (-1) + x^3 + 6\cdot x rightarrow 0 = (\left(1 + x\right) \cdot \left(1 + x\right) + 9)\cdot (x + 2\cdot (-1))\right) rightarrow x = 2

e^{|-z + x|} \cdot e^1 = e^{1 + |-z + x|}

8\cdot 7/10 - 5\cdot 3/10 = \frac{41}{10}

nx\cdot 2 - n^2 = x^2 - \left(x - n\right)^2

\frac{x}{x^3} = \frac{x}{x\cdot x\cdot x} = \dfrac{1}{x^2}

2/12 = \frac16

13/12 \cdot \pi - \pi/3 = \pi \cdot 3/4

\dfrac{2}{n^2 - n \cdot 16 + 63} = \frac{2}{(n + 9 \cdot (-1)) \cdot (n + 7 \cdot (-1))}

6 \cdot 15 \cdot 3^7 = 3^9 \cdot 2 \cdot 5

\frac{1}{x^2 + x \cdot 5 + 4} \cdot (-9 \cdot x + 24 \cdot \left(-1\right)) = -\frac{5}{1 + x} - \frac{4}{x + 4}

\dfrac{(-1+5i) \cdot (1+i)}{(1-i) \cdot (1+i)} = \dfrac{(-1+5i) \cdot (1+i)}{1^2 - (-1i)^2}

1/(a*b) = 1/(b*a) \neq 1/(a*b)

\dfrac{1}{9\cdot a + 6\cdot \left(-1\right)}\cdot 6\cdot \frac{4}{4} = \dfrac{24}{36\cdot a + 24\cdot (-1)}

(-3)\cdot 2 = 2\cdot \left(-1\right) - 2 + 2\cdot (-1)

\frac{1}{4}3\cdot \frac{1}{3}2/2 = 1/4

(1 + m) m! = \left(m + 1\right)!

f + e \neq 0\Longrightarrow -e \neq f

2 = 1/x + x \implies x = 1

\sin\left(2\cdot z\right) = \sin(z)\cdot \cos(z)\cdot 2

a + (1 + l) \cdot z = y \Rightarrow \frac{-a + y}{1 + l} = z

2/3 + \frac76 = \frac{11}{6} = \frac{5}{3} + 1/6

1/(h_2 h_1) = \frac{1}{h_2 h_1}

2\sqrt{5} = \sqrt{20}

\frac16 6 \frac{1}{6 (-1) + k} (2 (-1) - k*5) = \tfrac{1}{36 (-1) + k*6} (-30 k + 12 (-1))

x\cdot v = v^W\cdot x = x^W\cdot v

\frac12*(4^2 + 4*\left(-1\right)) = 6

2k + 1 = (k + 1)^2 - k^2

10 = \frac{1}{4\cdot a^2}\cdot h^2\cdot a - \tfrac{1}{2\cdot a}\cdot h\cdot h + c = -h^2/(4\cdot a) + c

z^2 + z + 1 + 2*(-1) = z * z + z + \left(-1\right) \neq (z + \left(-1\right))*(z + 2)

x \cdot \left(1 - 0.95^6\right) = -x \cdot 0.95^6 + x

160 + x = 11\cdot (x + 10) \implies 110 + 11\cdot x = 160 + x

\frac{1}{2(-1) + n}(n\cdot 3 + 3(-1)) \frac144 = \frac{1}{4n + 8(-1)}(12 n + 12 \left(-1\right))

\frac6y \leq -8\Longrightarrow y \geq -\frac68 = -3/4

\frac{10}{21} = 5/7\cdot \frac23

5555\cdot \cdots = 5/9

\tan\left(\frac{\pi}{4} + x\right) = \cot(\pi/4 - x)

0 = -\cos(2\cdot \pi) + 1

\frac{1/\left(\sqrt{2}\right)*\frac{2}{\sqrt{2}}}{2} = \frac12

\left(4 \cdot 11\right)^{1/2} + (16 \cdot 11)^{1/2} = 44^{1/2} + 176^{1/2}

1/2 + \dfrac{5^{\frac{1}{2}}}{2} = \tfrac12 \cdot (5^{\frac{1}{2}} + 1)

n = \dfrac{n}{1}

E_{n}*\dots*E_{1}*E_{n+1}*B = I \Rightarrow I = B*E_{n+1}*E_{n}*\dots*E_{1}

a/(h_2) + c/(h_1) = \left(c\cdot h_2 + a\cdot h_1\right)/(h_1\cdot h_2) + 0

-2\cdot x^2 + 1 + x = (1 + 2\cdot x)\cdot (-x + 1)

n^2 = 9 \cdot k \cdot k + 12 \cdot k + 4 = 3 \cdot (3 \cdot k^2 + 4 \cdot k + 1) + 1\Longrightarrow n^2 + (-1) = 3 \cdot \left(1 + k \cdot k \cdot 3 + k \cdot 4\right)

-\sin(\beta) \times \cos(x) + \sin(x) \times \cos(\beta) = \sin\left(-\beta + x\right)

\sqrt{5} \cdot \frac{10}{5} \cdot \sqrt{30} = \sqrt{6} \cdot 10

-2 \cdot \pi + \dfrac{17}{6} \cdot \pi = \dfrac{1}{6} \cdot 5 \cdot \pi

x + 4 + \dfrac{7}{4(-1) + x} = \frac{9\left(-1\right) + x^2}{x + 4(-1)}

\frac{20\cdot (q + 7\cdot (-1))}{16\cdot (q + 10)\cdot (q + 7\cdot (-1))} + \frac{16\cdot (q + 10)}{(7\cdot (-1) + q)\cdot (q + 10)\cdot 16} - \frac{1}{16\cdot (10 + q)\cdot (q + 7\cdot \left(-1\right))}\cdot 48 = \frac{1}{(q + 7\cdot (-1))\cdot (10 + q)\cdot 16}\cdot \left(20\cdot (7\cdot \left(-1\right) + q) + 16\cdot (q + 10) + 48\cdot (-1)\right)

\cos{3 \cdot \theta} = -3 \cdot \cos{\theta} + \cos^3{\theta} \cdot 4

\frac178 = 24/21

-r r r + (1 + r)^3 = 1 + 3 r^2 + 3 r

\frac{1}{-z \cdot 3 + 9 \cdot \left(-1\right)} \cdot (-z \cdot 3 + 9 \cdot (-1)) \cdot (-7/4) = \frac{21 \cdot z + 63}{-z \cdot 12 + 36 \cdot (-1)}

1/45 = \frac{p}{12 \cdot \pi} \cdot 12 \cdot \pi = p

10 + (-1) = 9 \neq 1

(p + t)^2 = p^2 + 2 \cdot p \cdot t + t^2

5/83 = \frac{\binom{13}{4}}{\binom{13}{4} + \binom{13}{3}\cdot 39}

\sin{2\cdot \dfrac{\pi}{2}} = 0

\frac{1}{44} = -\frac{1}{11} + \dfrac{1}{33} + \frac{1}{12}

-k^2*y^2 + z^2 = 1 \Rightarrow 1 = (k*y + z)*(z - k*y)

1 - (1 - \frac{1}{13})^5 = 122461/371293

11^{1/2}\cdot 4 + 11^{1/2} = 11^{1/2}\cdot 16^{1/2} + 11^{1/2}

\frac{z + 6}{3 \cdot (-1) + 9 \cdot z} \cdot 9/9 = \dfrac{9 \cdot z + 54}{z \cdot 81 + 27 \cdot (-1)}

\left(3^{1/2} + 7^{1/2}\right)^2 = 10 + 21^{1/2}\cdot 2

\left(1 = (-\sin{y} + 1)/2 \implies \sin{y} = -1\right) \implies y = \frac{\pi}{2} \cdot 3

\frac{3*z^2 + 3*z + 6*(-1)}{2*z^2 + 6*z + 4} = \dfrac{3*(z * z + z + 2*(-1))}{2*(z * z + 3*z + 2)} = \frac{3*(z + 2)*\left(z + (-1)\right)}{2*(z + 1)*(z + 2)}*1

0 + x + w + 0 = 0 + 0 + w + x \implies x + w = w + x

\frac{7}{6}\cdot \frac{1}{p + 6\cdot (-1)}\cdot (p + 6\cdot (-1)) = \dfrac{7\cdot p + 42\cdot \left(-1\right)}{6\cdot p + 36\cdot \left(-1\right)}

4 \cdot 4 + 1^2 + 2^2 + 3^2 = (1 + 2 + 3 + 4) \cdot 3

(e^z - e^{-z})/2 = 2 \implies -e^{-z} + e^z = 4

\frac33 \cdot \frac{5 \cdot z}{9 + 8 \cdot z} = \dfrac{z \cdot 15}{24 \cdot z + 27}

\sum_{n=1}^\infty \frac{1}{n*4^n} 3 (3 + 1)^n = \sum_{n=1}^\infty \dfrac{3*4^n}{n*4^n} 1 = \sum_{n=1}^\infty 3/n = 3 \sum_{n=1}^\infty 1/n

8 \cdot s^3 - 12 \cdot s \cdot s + 6 \cdot s + (-1) = 16 \cdot s^3 - 48 \cdot s^2 + 48 \cdot s + 16 \cdot (-1) = 24 \cdot s \cdot s \cdot s - 108 \cdot s^2 + 162 \cdot s + 81 \cdot (-1)

x\times (-1) = -x

5/15 \cdot \frac{6}{16} = \frac{1}{8}

\left((-1) + x^2\right)^3 = x^6 - 3*x^4 + 3*x^2 + \left(-1\right)

y^2 - 5 \cdot y + 6 = \left(2 \cdot (-1) + y\right) \cdot (y + 3 \cdot (-1))

6/10 + 2/100 = 2/100 + 60/100

\dfrac{1}{2(\frac12 + (-1)) (2(-1) + \frac12) \ldots*(1 + 1/2 - n) n!} = {\frac{1}{2} \choose n}

y = e \cdot y = y \cdot e

-x \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 + 2 \cdot 3 \cdot 3 \cdot 5 = 90 - 72 \cdot x

(-g) * (-g) = g^2

v v - v + 1 = \left(-\frac{1}{2} + v\right)^2 + \dfrac14 3

C_J \cdot x_J = C_J \cdot x_J

\sqrt{x + 3 \left(-1\right)} = \sqrt{-(3 - x)} = i \sqrt{3 - x}

((-3) \cdot z)/(\sqrt{z}) = -\sqrt{z} \cdot 3

8^{8^8} + 1 = (1 + 2^{2^{25}} - 2^{2^{24}}) \cdot (2^{2^{24}} + 1)