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Dresden Database Research Group 12

\frac{1}{2} \cdot (3 + 5^{1/2}) = \frac{3}{2} + 5^{1/2}/2

\left(\sqrt{a}\cdot \sqrt{b}\right)^2 = (\sqrt{a\cdot b})^2

10010 = 2 \cdot 5 \cdot 7 \cdot 11 \cdot 13

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

\dfrac{79.2}{10^7} = \frac{1}{10^7} \cdot 79.2

\frac{\partial}{\partial x} (w \cdot x) = w \cdot \frac{dx}{dx} + x \cdot \frac{dw}{dx}

\dfrac{6}{8} \cdot \dfrac{1}{10 \cdot 9} \cdot \dfrac57 \cdot 24 \cdot 3 = 3/7

x > -s + s_n \Rightarrow s + x > s_n

(p^x + 3) \cdot (p^x + \left(-1\right)) + 4 = p^{2 \cdot x} + 2 \cdot p^x + 1 = (p^x + 1)^2

\frac{2}{(x + 8) (6 + x)} \frac{2}{2} = \frac{1}{2(8 + x) (x + 6)}4

(n + 1)*2 + (-1) = 1 + 2*n

x^4 + 4 = x^4 + 4\cdot x^2 + 4 - 4\cdot x^2 = (x \cdot x + 2)^2 - \left(2\cdot x\right)^2 = (x^2 - 2\cdot x + 2)\cdot (x \cdot x + 2\cdot x + 2)

-1/2 (-\frac14) = 1/8

m = \frac{3}{2} \cdot y\Longrightarrow y = 2/3 \cdot m

\frac{1}{(1 + 1)*(1 + 2)*4}*(3 + 1) = 1/(3*1*2)

y/3\cdot 3 = y

-e^{32} + 384*\left(-1\right) = -384 - e^{32}

-24 = -x + 2 \cdot \left(-1\right) + 4 = -x + 2

\dfrac{30}{7} = \frac{(4 + 1)\cdot 6}{1 + 6}

36 = (6\cdot (-1) + 30 + 12\cdot (-1))\cdot 3

1/y = \frac{1}{y \times \overline{y}} \times \overline{y}

\left(17 + 3 \cdot \sqrt{34}\right) \cdot \left(17 - 3 \cdot \sqrt{34}\right) = -17

60 = (25 - 6 d) (25 - 4 d) - (25 - 7 d) (25 - 2 d) = 25 - 10 d

1 + {n + 1 \choose n} = {n + 2 \choose n + 1}

(g + d)/2 = (2\cdot g + d - g)/2 = g + \dfrac{1}{2}\cdot \left(d - g\right)

7/7 \cdot \frac{1}{-3} \cdot (8 \cdot x + 7 \cdot (-1)) = \dfrac{1}{-21} \cdot (56 \cdot x + 49 \cdot (-1))

e^{14*3 \pi i/4} = (e^{\frac{1}{4} \pi i*3})^{14}

\frac{x}{\sqrt{x \cdot x + h}\cdot 2}\cdot 2 = \frac{1}{\sqrt{x^2 + h}}\cdot x

\frac{1}{\sqrt{f} + \sqrt{a}} \cdot (f - a) = -\sqrt{a} + \sqrt{f}

-60*348*t + t*20915 = 35*t

-9/(-9)*(-1/7) = 9/(-63)

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

a \cdot b = \frac{1}{1/a \cdot 1/b} = \frac{1}{1/b \cdot 1/a} = b \cdot a

c + g + x = x + c + g

\lim_{h \to 0} \left(y^2 + 2yh + h^2 - y^2\right)/h = \lim_{h \to 0} \frac{1}{h}\left(h^2 + 2hy\right)

(1 + 2/k)^k = (\frac1k\cdot (k + 2))^k = \left(\frac{k + 2}{k + 1}\right)^k\cdot ((k + 1)/k)^k

\cot(\frac{\pi}{4} - z) = \tan(z + \frac{\pi}{4})

-(1 + a'^2 + 3a') + a^2 + 3a + 1 = (a - a') (3 + a + a')

(-2)^2 - 4y^2 = 4(1-y^2)

-1/11 + 4/11 = \frac{3}{11}

\left(3 + z\right)*(z + 2) = 6 + z^2 + 5*z

(1 + r) \cdot (r + 6) = 6 + r^2 + 7 \cdot r

\mathbb{P}(x) = \mathbb{P}(x)\cdot \cos{x} \implies \cos{x} = 1

0 + 0 + 3\cdot \frac{1}{3}\cdot t = t

4 \cdot a = (a + 1 + x)^2 = a^2 + 2 \cdot (1 + x) \cdot a + (1 + x) \cdot (1 + x)

\frac{1}{c_1 c_2} = 1/(c_1 c_2)

x^{1/c} = x^{\dfrac1c}

36 X - N = 35 X - N - X

(h + b)^2 = b^2 + h^2 + 2 b h

C_2*C_1^l = C_2*C_1^l

\dfrac{5 + w}{w^2 - w \cdot 8 + 15} = -\dfrac{4}{w + 3 \cdot (-1)} + \frac{5}{5 \cdot (-1) + w}

72 = 9(-1) + 9^2

f + e + x = f + e + x

\frac16 6 (-\dfrac{1}{t + 9 (-1)} 2) = -\frac{12}{54 \left(-1\right) + 6 t}

\dfrac{1}{10 + 5 \cdot t} \cdot 3 = \frac{1}{5 \cdot (2 + t)} \cdot 3

-1/6 - \frac{7}{4} = -1*2/(6*2) - 7*3/(4*3) = -\frac{1}{12}2 - 21/12 = -(2 + 21 (-1))/12 = -23/12

\dfrac12 \cdot (1 + 5^{1/2}) = \dfrac12 + 5^{1/2}/2

\sin2A+\sin2B+2\sin(A+B)=\cdots=4\sin(A+B)\cdot\sin^2\dfrac{A-B}2

\frac{4 + \tfrac3x}{-5/x + 7} = \dfrac{1}{7x + 5(-1)}(4x + 3)

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

12\cdot b = 11 + \frac{1}{3\cdot b}\cdot 24 + 12\cdot (-1) \implies 12\cdot b = (-1) + 8/b

18 + l^2 + l \cdot 11 = \left(l + 9\right) \cdot (l + 2)

\frac{1}{z*4 + 36 (-1)} 3 = \dfrac{1}{4 \left(z + 9 (-1)\right)} 3

\frac{24 - 8\cdot m}{m\cdot 5 + 15\cdot (-1)} = \frac{1}{m + 3\cdot (-1)}\cdot (3\cdot (-1) + m)\cdot (-8/5)

1 - 99/100\cdot 98/99\cdot 97/98\cdot 96/97\cdot \frac{95}{96} = 1 - 0.95 = 0.05 = \frac{1}{20}

-2 = -2(-5z) - 16 = 10 z - 16 = 10 z + 16 (-1)

x^0 e^{xq} = e^{qx}

\dfrac{1}{b \times h} = \frac{1}{h \times b}

2.56\cdot 10 = \frac{25.6}{10^6}\cdot 1 = \frac{2.56}{10^5}

\frac55\cdot \frac{7 + 4\cdot x}{6 + 3\cdot x} = \frac{1}{15\cdot x + 30}\cdot (20\cdot x + 35)

1/3 + \frac13 = \dfrac{2}{3}

-(e\cdot i\cdot z/2 - e^{\left((-1)\cdot i\cdot z\right)/2})^2 = -\left(2\cdot i\right)^2\cdot \sin^2\left(z/2\right) = 4\cdot \sin^2(z/2)

24 + 9\left(-1\right) = 15

-1/((-1)\cdot \frac{1}{3}) = 3

\dfrac{7}{12} = \dfrac{1}{36 \cdot \pi} \cdot E_s \cdot 36 \cdot \pi = E_s

\frac{1}{\sqrt{\frac{1}{n} (n + \left(-1\right))} \sqrt{\frac1n ((-1) + n)}} (1/n*\left(-1\right)) = -\frac{1}{n + (-1)}

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

u = e^z + 2 \Rightarrow \frac{\text{d}u}{\text{d}z} = e^z = u + 2 \cdot (-1)

2\cdot (-1) + x^2 = \left(x + \sqrt{2}\right)\cdot (x - \sqrt{2})

\mathbb{E}[x\cdot I] = \sqrt{\mathbb{E}[x^2]\cdot \mathbb{E}[I^2]}

\left(w + x + y + z\right)^2 = 2*(w*z + x*y + x*z + w*x + z*y + y*w) + x^2 + y^2 + z^2 + w^2

\cos\left(-\pi \frac{1}{3}2\right) = -0.5

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

π \cdot (-\frac{8}{3} + 4 \cdot (-1) + 16) = π \cdot 28/3

180 \cdot 2 = 360

1 + 32/8 = 1 + 4 = 5

3/4*5/4 = \tfrac{1}{16}*15 = 0.9375

\frac{1}{10} \cdot 7 - 5 \cdot 9/10 = -38/10

6/6*\frac{2*t + 1}{15*t + 20} = \frac{t*12 + 6}{120 + t*90}

H + 2 = \frac{1}{H + 2*(-1)}*(H + 2)*(H + 2*\left(-1\right)) = \frac{1}{H + 2*(-1)}*\left(H^2 + 4*\left(-1\right)\right)

74 = 4 + 7\times 10 = 9 + 5\times 13

-x*(-\varepsilon) = x*\varepsilon

1/8 = \frac18*3*\frac{3}{9}

a^2 + d^2 - 2\cdot a\cdot d = (a - d) \cdot (a - d)

(1 - t^2)^{-k} (1 - t)^{-k} = (1 - t)^{-k} (1 + t)^{-k} (1 - t)^{-k} = (1 - t)^{-2k} (1 + t)^{-k}

30 = 10\cdot t + 16 + 50\cdot \left(-1\right) = 10\cdot t + 34\cdot \left(-1\right)

\|A + x\|^2 = qp\cdot (A + x)^W\cdot (A + x) = qp\cdot \left(A^W + x^W\right) (A + x) = qp\cdot (A^W A + A^W x + x^W A + x^W x)

-\frac128 = ((-8) \frac{1}{2})/\left(2\cdot \frac{1}{2}\right) = -4

\frac12\cdot (-(k + (-1)) + N)\cdot \left(-((-1) + k) + N + 1\right) = (N - k + 2)\cdot \left(N - k + 1\right)/2

(-1)^{\frac{1}{n}} = (e^{\pi\cdot i})^{1/n} = e^{\frac{\pi\cdot i}{n}\cdot 1}