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Dresden Database Research Group 14

V \cdot x^{1/2} = V \cdot x^{\dfrac12}

10! \cdot \tfrac{1}{3! \cdot 2! \cdot 2!}/10 = \dfrac{1}{2! \cdot 2! \cdot 3!} \cdot 9!

-\dfrac{6}{-1} = 6

\left(8 \times x + x = 45\Longrightarrow 45 = x \times 9\right)\Longrightarrow x = 5

\frac{1}{{4 \choose 2}} (-{2 \choose 2} + {3 \choose 2}) = \dfrac{1}{3}

y*2 |e| = y |e|*2

\frac{1}{8 \cdot (-1) + p \cdot 2} = \frac{1}{(p + 4 \cdot (-1)) \cdot 2}

1 = 84 + 83\cdot \left(-1\right)

x^2 = 9 \cdot x \cdot x = 3 \cdot 3 \cdot x \cdot x + 0

1/6 = -\frac{4}{3} + \frac{3}{2}

\sin{x\cdot 3} = \sin{(x + \dfrac{2}{3}\cdot \pi)\cdot 3}

1 + y + y^2 + y^3 = (y + 1)\times (y^2 + 1)

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

-2/4 + 1 = 2/4

( X_1, Y_1)\cdot ( X_2, Y_2)\cdot ( X_3, Y_3) = ( X_1\cdot X_2, Y_1\cdot X_2 + Y_2)\cdot ( X_3, Y_3) = ( X_1\cdot X_2\cdot X_3, (Y_1\cdot X_2 + Y_2)\cdot X_3 + Y_3) = ( X_1\cdot X_2\cdot X_3, Y_1\cdot X_2\cdot X_3 + Y_2\cdot X_3 + Y_3)

87 = \frac14 \cdot 348

\frac{7\cdot (-1) + 35}{(6 \cdot 6 + 3^2 + 2^2)^{\frac{1}{2}}} = 4

0.4\cdot n = (0.3 + 0.1)\cdot n

(-1) \cdot (-1) = (-1)\cdot (-1) = -1

\dfrac{-4 \cdot z + 11 \cdot (-1)}{4 \cdot \left(-1\right) + z^2 + 3 \cdot z} = -\frac{1}{z + 4} - \frac{1}{(-1) + z} \cdot 3

218^2 + \left(-1\right) = (218 + 1) \cdot \left(218 + (-1)\right) = 219 \cdot 217 = 3 \cdot 73 \cdot 7 \cdot 31

\binom{2 + i}{2} = \binom{i + 3}{3} - \binom{i + 2}{3}

x^{10} = (1 - x)*(13 - 21*x) = 21*x * x - 34*x + 13 = 21*(1 - x) - 34*x + 13 = 34 - 55*x

-2/11 + 4/11 = \tfrac{2}{11}

p\cdot 4 = 12 rightarrow p = 3

1/45 = \frac{F_s}{36\cdot \pi}\cdot 36\cdot \pi = F_s

-2 = (-1) + \eta \Rightarrow -1 = \eta

\dfrac{6}{6}*\dfrac{2}{(7 + a)*\left(8 + a\right)} = \frac{12}{6*\left(a + 7\right)*(a + 8)}

2(-1) - 9 = -11

\dfrac{-x*6 + 18}{x * x - x*4 + 5*(-1)} = -\frac{2}{5*(-1) + x} - \frac{4}{1 + x}

\frac{5 - x}{6 + x^2 - 5\cdot x} = -\frac{3}{x + 2\cdot (-1)} + \frac{1}{x + 3\cdot (-1)}\cdot 2

{2 \choose 1}\cdot {5 \choose 1}\cdot {4 \choose 1}\cdot {3 \choose 1}\cdot {1 \choose 1} = 120

1 + r + r \times r + ... + r^x = \frac{1 - r^{(-1) + x}}{1 - r}

e^{13*5i\pi/12} = (e^{5\pi i/12})^{13}

\frac{11}{30} = \dfrac{A_s}{4 \cdot \pi} \cdot 4 \cdot \pi = A_s

\frac{1}{36}*\left((-1) + 37 * 37 * 37\right) = 3*7*67

\frac{2}{3\times \left(-1\right) + \theta} - \frac{3}{\theta + 2\times \left(-1\right)} = \frac{1}{\theta^2 - \theta\times 5 + 6}\times \left(5 - \theta\right)

\frac{3}{4} = s/(16\cdot \pi)\cdot 16\cdot \pi = s

\binom{m}{2} \binom{2 \left(-1\right) + m}{j}/(\binom{m}{j}) = \binom{m - j}{2}

x^4 + 10 x^2 + 25 = \left(x * x + 5\right)^2 = (2*3^{1/2} x)^2 = 12 x^2

-7/5 \cdot \frac{(-1) + 5 \cdot x}{x \cdot 5 + (-1)} = \tfrac{-35 \cdot x + 7}{5 \cdot \left(-1\right) + x \cdot 25}

x - L + L^2 - L^3 + ... = \dfrac{1}{x + L}

-12^{\frac{1}{2}} = -2*3^{1 / 2}

\left(y + 9\right)/4\cdot 4/4 = \left(36 + y\cdot 4\right)/16

e^y = e^{(-1) + y} \cdot e

10/10 \cdot \frac{1}{5 \cdot r} \cdot (5 \cdot r + 2) = \frac{20 + r \cdot 50}{r \cdot 50}

(x^2)^4 = (x^4)^2 = (x + 1)^2 = x^2 + 1

\dfrac{1}{4}*2 = \frac{4}{8}

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

\frac{3}{(j + 5 \cdot (-1)) \cdot \left(j + 9 \cdot (-1)\right)} = \frac{3}{45 + j^2 - 14 \cdot j}

1/2 + 0 = \frac{2}{4} < 2/\pi

(x \cdot x \cdot x \cdot 4 - x^2 + 3)/x = 3/x + x^3 \cdot 4/x - \frac{x^2}{x}

\dfrac{d}{dx}\left(\dfrac{\sin(x)}{x^2}\right)=\dfrac{x\cos(x)-2\sin(x)}{x^3}

3.14 = \dfrac{157}{50} = \frac{1}{7} \cdot 22 - 1/350

\tan^2{x} + \sin^2{x} + \cos^2{x} = \frac{\text{d}}{\text{d}x} \tan{x}

\frac{x\cdot \frac{1}{y}}{z}\cdot 1 = \frac{x\cdot \frac1z}{y} = \tfrac{x}{y\cdot z}

\dfrac{1}{100}95 = 5*19/100

\dfrac{z^5}{z^2} = z^{5 + 2 \cdot (-1)} = z^3

\left(-Y*2 + Y^3\right)/Y = 2 (-1) + Y Y

\dfrac{9}{32} = 3/4*3/8

(-f + a)^2 = a^2 + f^2 - a \cdot f \cdot 2 rightarrow a^2 + f^2 - (-f + a)^2 = 2 \cdot a \cdot f

X\cdot z = X\cdot z

\frac{17}{12} \pi + 0 = \pi*17/12

\left(-1\right) + 11/12 = -1/12

0 = y + 2 (-1) rightarrow 2 = y

\sin(x) = -\cos(\dfrac{\pi}{2} + x)

47*((-1) + x*47) = 47^2 x + 47 (-1)

11 r + 33 (-1) = -11\cdot 3 + 11 r

2\cdot (2 + z) = 2\cdot z + 4

-\frac{36}{-8} = -4/\left(-4\right)\cdot \frac12\cdot 9

C*Q * Q = Q^2*C

\frac{1}{7} \cdot 10 = \frac{1}{28} \cdot 40

0 = \dfrac{1}{7} \cdot 2 \cdot 0

\frac{1}{2^k}\cdot 2 = \frac{1}{\frac12\cdot 2^k}

27 \left(-1\right) + s \cdot s + 6s = (9 + s) (3\left(-1\right) + s)

-\frac{14}{7 c + 42 (-1)} = \frac{7}{7} (-\dfrac{2}{c + 6 (-1)})

-\dfrac14 = ((-1)\cdot 1/2)/2

\frac13/(1/3) = 1

4 = 2*x^2*\left(1 - \frac17\right) = 12/7*x^2

5 + 2 \sqrt{13} = \left(a + b \sqrt{13}\right) \left(a + b \sqrt{13}\right) \left(a + b \sqrt{13}\right) = a^2 a + 39 a b^2 + (3 a^2 b + 13 b^3) \sqrt{13}

\frac{k \cdot k \cdot k\cdot 120}{80\cdot k \cdot k \cdot k} = 120/80\cdot \frac{1}{k^3}\cdot k \cdot k \cdot k

\frac{1}{b}\cdot a + g/h = \frac{1}{b\cdot h}\cdot (a\cdot h + b\cdot g) \neq a\cdot h + b\cdot g

\frac{36 \cdot \left(-1\right) - i \cdot 4}{4 \cdot i + 12 \cdot (-1)} = 4/4 \cdot \dfrac{-i + 9 \cdot (-1)}{3 \cdot (-1) + i}

1 + \frac{1}{1 + 1/\left(5\cdot \frac{1}{3}\right)} = 1 + \frac{1}{1 + \frac{1}{1 + \frac23}}

11 * 11*3^2 = 1089

b \times a = a^3 \times b = a \times a \times a \times b = a \times b

5\cdot K = K + K + K + K + K

\frac{1}{(1 + z)^2} z = \dfrac{1 + z + (-1)}{(1 + z)^2} = \frac{1}{1 + z} - \frac{1}{(1 + z)^2}

\frac{(\frac{1}{q^4})^5}{\frac{1}{p \cdot p^2}\cdot \tfrac{1}{q}} = \dfrac{1}{q^{20}\cdot \frac{1}{q\cdot p^3}}

\tfrac{l}{8 \cdot \left(-1\right) + l \cdot 2} \cdot 14 = \frac{2}{2} \cdot \frac{7 \cdot l}{l + 4 \cdot (-1)}

\tfrac{90}{x\cdot 10}\cdot x^4 = \frac{x^4}{x}\cdot 90/10

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

\frac{2 \cdot p}{\left(p + 2\right) \cdot (2 + p)} \cdot 1 = \dfrac{2 \cdot p}{4 + p^2 + p \cdot 4}

1/6 = 5/9\cdot 6/10\cdot \frac{1}{8}\cdot 4

-\sqrt{7} + \sqrt{9\cdot 7} = -\sqrt{7} + \sqrt{63}

6\cdot (-1) + x \cdot x + x = (2\cdot (-1) + x)\cdot (x + 3)

t^4 - t^2 + 2(-1) = (t^2 + 2(-1)) (1 + t^2)

\left(\frac{z}{c}\right)^2 = (z/c)^2

-\pi \cdot 24 + \frac{76}{3} \pi = \pi \frac43

x + iy - z + ik = x - iy + (z - ik) (x - z) + y - k = x + z - y - k