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11,077 | 2 \cdot 2^{x + 1} + (-1) - 2^x = 3 \cdot 2^x + \left(-1\right) > 2 \cdot 2^x + (-1) |
26,646 | Y^2 + 4Y + 4 = \left(Y + 2\right)^2 = 0\Longrightarrow Y = -2 |
14,625 | n\cdot x\cdot g = \frac{1}{2}\cdot x^2\cdot k\Longrightarrow x = 2\cdot n\cdot g/k = 0.126\cdot n |
-15,899 | -7\cdot \frac{4}{10} + 6\cdot \frac{1}{10}\cdot 6 = 8/10 |
49,251 | 6! \cdot 7 \cdot 6 \cdot 5 = 151,200 |
-27,563 | \frac{dz}{dT} = \frac{1}{\left(-1\right) (5 T + 2 z)} ((-1) \left(6 T^2 - 5 z\right)) = \dfrac{1}{5 T + 2 z} \left(6 T T - 5 z\right) |
-6,342 | \frac{4}{y \cdot y - 13 \cdot y + 42} = \frac{4}{\left(y + 6 \cdot (-1)\right) \cdot (7 \cdot \left(-1\right) + y)} |
25,961 | c^{\dfrac{p}{q}} \cdot c^{t_2/(t_1)} = c^{\frac{1}{q \cdot t_1} \cdot (p \cdot t_1 + t_2 \cdot q)} = c^{p/q + \frac{t_2}{t_1}} |
8,988 | 1 = w_j^3 \Rightarrow \left(-w_j\right) * \left(-w_j\right) * \left(-w_j\right) = -w_j^3 = -1 |
-13,930 | \frac{1}{6 + 3}72 = 72/9 = \frac1972 = 8 |
13,887 | -347 + 5 \cdot \left(-1\right) = -352 |
29,445 | 6 = 2*3 = (4 - 10^{\frac{1}{2}}) (4 + 10^{\frac{1}{2}}) |
4,883 | a^{x - z} = \dfrac{a^x}{a^z} |
-10,754 | 10 = -6 + 5*f + 7*(-1) = 5*f + 13*(-1) |
1,818 | e^y\times e^{z'} = e^{y + z'} |
3,653 | n + 6\cdot n^2 = (1 + 6\cdot n)\cdot n |
25,152 | \frac59 \cdot 6/10 = \frac{1}{3} |
12,792 | (x' + z')^2 - (x' - z') \cdot (x' - z') = x' z' \cdot 4 |
11,213 | z + 6 = \sqrt{x \cdot x + z \cdot z}\Longrightarrow x^2 = z\cdot 12 + 36 |
-10,619 | \frac{1}{9 + 6 \cdot x} \cdot 8 \cdot \dfrac44 = \tfrac{32}{36 + x \cdot 24} |
30,621 | x*e = x\Longrightarrow x*e = x |
782 | 4^{\left(-1\right) + n} \cdot 4 = 4^n |
-2,835 | 16^{\frac{1}{2}} \cdot 3^{\frac{1}{2}} + 9^{\dfrac{1}{2}} \cdot 3^{1 / 2} = 3^{1 / 2} \cdot 4 + 3 \cdot 3^{\frac{1}{2}} |
23,621 | 1 + (-1) + 2\cdot \cos^2(x) = 0 + 2\cdot \cos^2(x) = 2\cdot \cos^2\left(x\right) |
2,087 | (y^4 + y^3 + y^2 + y + 1) (y + (-1)) = y^5 + (-1) |
17,245 | \frac{1}{-z + 1}*z^2 = z^2 + z^3 + z^4 + \cdots |
6,103 | r\cdot (x + z) = z\cdot r + r\cdot x |
-2,906 | \sqrt{13}\cdot \left((-1) + 2\right) = \sqrt{13} |
29,085 | x^3 + 1 = \left(x + 1\right) (1 + x^2 - x) |
15,078 | 2*(-1) + \frac1D*3 = 3*\left(-1\right) + (D + 3)/D |
12,055 | x\cdot \tfrac{\sin(\|x\|\cdot k)}{k\cdot \|x\|}\cdot k^2 = \sin(k\cdot \|x\|)\cdot \frac{x}{\|x\|}\cdot k |
9,865 | \cot{\varphi} = \tan(\frac{\pi}{2} - \varphi) |
-7,960 | \tfrac{7 - i \times 24}{-4 \times i - 3} = \frac{1}{-3 - 4 \times i} \times (7 - i \times 24) \times \frac{1}{i \times 4 - 3} \times (-3 + 4 \times i) |
14,552 | \dfrac{2 + 2*\sin{D}}{\cos{D}*(1 + \sin{D})} = \frac{2}{\cos{D}} = 2*\sec{D} |
25,009 | \cos(x) = \frac{1}{2} \cdot (e^{i \cdot x} + e^{-i \cdot x}) = \cosh\left(i \cdot x\right) |
-14,320 | \dfrac{28}{7 + 3 (-1)} = \frac{28}{4} = \frac{1}{4} 28 = 7 |
37,796 | \operatorname{E}[W_1\cdot W_2] = \operatorname{E}[W_1]\cdot \operatorname{E}[W_2] |
-3,963 | \frac{1/2*5}{k^3} = \tfrac{1}{2*k * k^2}*5 |
6,077 | (2^{\frac{1}{2}} + y^2)\cdot (-2^{\frac{1}{2}} + y^2) = y^4 + 2\cdot \left(-1\right) |
-9,379 | 3 - i \cdot 2 \cdot 3 = 3 - 6 \cdot i |
-6,478 | \frac{2}{3\cdot x + 3\cdot (-1)} = \dfrac{1}{\left((-1) + x\right)\cdot 3}\cdot 2 |
-10,310 | \frac55\cdot (-\dfrac{1}{m\cdot 6 + 6\cdot (-1)}) = -\frac{5}{30\cdot m + 30\cdot (-1)} |
9,011 | 1/\cos(\arcsin(x)) = d/dx \arcsin(x) |
-3,024 | (9 \cdot 7)^{1 / 2} + (4 \cdot 7)^{1 / 2} = 28^{1 / 2} + 63^{\tfrac{1}{2}} |
6,111 | (1 + 2/n)^n = (\frac{1}{n}*(n + 2))^n = (\frac{n + 2}{n + 1})^n*((n + 1)/n)^n |
17,245 | \frac{1}{1 - y} \cdot y \cdot y = y^2 + y \cdot y \cdot y + y^4 + \cdots |
9,873 | \mathbb{N}_{k} \coloneqq \left\{1, k, \cdots\right\} |
15,898 | \frac{5}{18} = \frac{5}{4 + 5} \frac{1}{4 + 5 + \left(-1\right)}\left(5 + (-1)\right) |
-4,423 | \dfrac{1}{y + 5} + \frac{2}{\left(-1\right) + y} = \frac{9 + y*3}{y^2 + 4y + 5(-1)} |
38,021 | 0 = -(0 + 0\cdot \left(-1\right)) |
18,164 | \frac{13}{3!} \cdot 12 \cdot 11 = {13 \choose 3} |
13,428 | (f + b)^2 = 2fb + f^2 + b^2 |
12,828 | 2\cdot u = (1 + u)\cdot (1 - u^2) = 1 - u^3 - u \cdot u + u |
434 | -\frac{1}{z + 1} = \frac{1}{(2 + z) (z + 1)}z - \dfrac{2}{z + 2} |
45,277 | 48 = 3\times 2^4 |
-22,227 | y^2 + y\cdot 16 + 63 = (7 + y)\cdot \left(y + 9\right) |
1,393 | \mathbb{E}[(R + V)^2] = \mathbb{E}[R^2] + \mathbb{E}[V^2] + 2*\mathbb{E}[V*R] |
40,462 | \lim_{x \to 3} \frac{1}{3 - x} \cdot (2 \cdot x - e^{x + 3 \cdot (-1)} + 5 \cdot (-1)) = \dfrac{1}{(-1) \cdot (x + 3 \cdot (-1))} \cdot \left(-e^{x + 3 \cdot (-1)} - 5 + 2 \cdot x\right) = \frac{1}{\left(-1\right) \cdot (x + 3 \cdot (-1))} \cdot ((-1) \cdot \left(e^{x + 3 \cdot (-1)} - -5 + 2 \cdot x\right)) = \frac{1}{(-1) \cdot y} \cdot ((-1) \cdot (e^y - -5 + 2 \cdot x)) = (e^y - -5 + 2 \cdot x)/y |
32,019 | b \cdot b \cdot b + 1 = (b^2 - b + 1) (1 + b) |
11,630 | \sum_{k=1}^n ((-1) + k) \cdot (1 + k) = \sum_{k=1}^n (\left(-1\right) + k^2) |
48,244 | 8 = 2^2 \cdot 2 \cdot 5^0 |
17,795 | \dfrac{1}{d/h + z} \cdot (b/a + z) \cdot a/h = \frac{a \cdot z + b}{z \cdot h + d} |
2,391 | Y_2 Y_1 + B = Y_1 \implies B = Y_1 - Y_2 Y_1 |
54,189 | X = X |
16,196 | \frac{\frac{2}{31}}{25} = \frac{2}{775} |
27,447 | \dfrac{\dfrac{1}{19^{20}}}{\frac{1}{20^{20}}} \cdot 1 = \dfrac{20^{20}}{19^{20}} \approx 2.79 |
-29,592 | \frac{d}{dz} (2\cdot z^2) = 2\cdot d/dz z^2 = 2\cdot 2\cdot z^1 = 4\cdot z |
820 | \tan(\frac{\pi}{8}) = (-1) + 2^{1 / 2} |
-7,030 | \frac{5}{21} = \frac{4}{7} \cdot \frac19 \cdot 6 \cdot 5/8 |
-11,458 | -4 + 12 + i\cdot 19 = 8 + i\cdot 19 |
28,182 | 1 + y*2 = 2*x + 1 \implies x = y |
27,714 | (h + 1)^2*d = (h^2 + 2*h + 1)*d = h^2*d + 2*h*d + d = h*d*h + h*d + h*d + d |
-10,707 | -\frac{1}{a\cdot 48 + 48}\cdot (a\cdot 16 + 20\cdot (-1)) = \dfrac14\cdot 4\cdot (-\dfrac{1}{12 + a\cdot 12}\cdot (a\cdot 4 + 5\cdot \left(-1\right))) |
23,843 | 25=(-1) \times(-25) |
11,444 | ad = \frac{1}{4}(-(a - d) * (a - d) + \left(d + a\right)^2) |
-7,219 | \dfrac{1}{15}\cdot 2 = 3/9\cdot \dfrac{1}{10}\cdot 4 |
-1,491 | -5/3*2/9 = \frac{1}{9*\dfrac{1}{2}}*((-5)*\frac{1}{3}) |
-20,788 | \frac{1}{5 + l\cdot 5}\cdot (7\cdot (-1) - 7\cdot l) = \frac{1}{l + 1}\cdot \left(l + 1\right)\cdot (-7/5) |
3,015 | 1 = 1/\left(25\cdot x\right) \Rightarrow x = \frac{1}{25} |
32,217 | {4 \choose 2} = \dfrac{3}{2!}4 = 6 |
27,856 | 88 = (-1) + 89 |
16,070 | 8/3 = \frac{40}{60} + 2 |
32,489 | e^{x + 1} = e*e^x \geq 2*e^x |
33,984 | 2*9*11 = 198 |
2,549 | y \cdot y + x \cdot x + x \cdot y \cdot 2 = \left(x + y\right)^2 |
2,220 | (12 + 1)*(1 + 6) = 91 |
8,530 | \frac{1}{N^N}(N + (-1))^N = (\frac{1}{N}(N + (-1)))^N = (1 - \frac{1}{N})^N |
7,406 | 1680/71 = 23 + \frac{1}{71}47 |
-20,105 | \frac{7 + 49 q}{q\cdot 28 + 4} = \tfrac{1 + 7q}{q\cdot 7 + 1}\cdot \frac147 |
-18,133 | 13*\left(-1\right) + 14 = 1 |
34,326 | 0 + 4/9 + 2 \cdot \frac13 = \tfrac{1}{9} \cdot 10 |
-7,658 | \frac{22\cdot i - 7}{i\cdot 3 + 2} = \frac{-7 + i\cdot 22}{i\cdot 3 + 2}\cdot \frac{-i\cdot 3 + 2}{2 - 3\cdot i} |
18,302 | \frac{\sin(7\pi)}{\sin(4\pi)} = \dfrac{0}{0} = 1 |
17,522 | 2\cdot 3^2 + 3\cdot (\frac{7}{2}) \cdot (\frac{7}{2}) = \dfrac{219}{4} \neq 17 |
4,263 | 3^3 - 3\cdot 3^2 + 3\cdot (-1) + 3 = 3^3 - 3^3 + 0 = 0 |
8,058 | (a + c^{\frac{1}{2}}\cdot b) \cdot (a + c^{\frac{1}{2}}\cdot b) = a^2 + c\cdot b^2 + a\cdot c^{1 / 2}\cdot b\cdot 2 |
41,119 | H_1 = \begin{pmatrix}1 & 2\\3 & 4\end{pmatrix} = H_2^2 \Rightarrow det\left(H_1\right) = det\left(H_2^2\right) = det\left(H_2\right)^2 |
26,665 | {n \choose 2} - {n + (-1) \choose 2} = (n + (-1)) \cdot (n - n + 2 \cdot (-1))/2 = n + (-1) |
42,273 | 10/15 = \tfrac{2}{3} |
20,405 | 1 = 1 + 0\times i |
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