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25,753 | \frac{s\cdot (-10)}{(s^2 + 1)\cdot \left(s \cdot s + 2\right)} = \frac{s\cdot 10}{s^2 + 2} - \dfrac{10\cdot s}{s^2 + 1} |
-9,233 | 11 \cdot n^2 = 11 \cdot n \cdot n |
28,879 | \frac{2}{1.5 + 2} = \frac17\cdot 4 |
31,621 | (x*G + Z*G + Z*x)/\left(Z*G*x\right) = \frac{1}{x} + 1/Z + \frac1G |
-26,654 | 3\cdot y^2 - 20\cdot y + 7\cdot (-1) = (y\cdot 3 + 1)\cdot (y + 7\cdot (-1)) |
19,605 | 1/\left(b\cdot d\right) = 1/(d\cdot b) |
3,089 | xg_2 - xg_1 = (g_2 - g_1) x |
17,979 | \tfrac{f - b - c}{c + f - b} = \frac{1 - \frac{1}{f - b}*c}{1 + \frac{c}{f - b}} |
9,164 | 2 = x^{15} \Rightarrow x^{45} = 8 |
23,344 | y-x+1=y-(x-1) |
-2,237 | 7/12 - \dfrac{5}{12} = \frac{2}{12} |
-4,266 | \frac25 \times n = 2 \times n/5 |
-2,731 | \sqrt{16 \cdot 5} - \sqrt{4 \cdot 5} = \sqrt{80} - \sqrt{20} |
20,465 | 540 = \binom{3}{2} \binom{1}{1} \binom{4}{2} \binom{2}{2}*3! \binom{5}{1} |
16,852 | 4^{m + 1} + (-1) = 4*4^m + (-1) = 3*4^m + 4^m + (-1) |
6,912 | \sin(v\cdot 2) = 2\cdot \sin(v)\cdot \cos(v) |
-20,378 | \frac{1}{k*(-36)} (-k*30 + 12 (-1)) = \left(-k*5 + 2 (-1)\right)/\left((-6) k\right)*6/6 |
30,415 | \cos{x} \sin{z} + \cos{z} \sin{x} = \sin(x + z) |
31,052 | 1 + x^6 = (x^4 + 1 - x^2) \cdot (x^2 + 1) |
39,136 | -6 - 9*9*3 + 2*3 + 3*27 = 27 (-9) + 3*27 = 27 (-6) = -162 |
17,212 | 3 \cdot y^2 + 2 = 3 \cdot (y \cdot y + (-1)) = 3 \cdot \left(y + (-1)\right) \cdot (y + 1) = 3 \cdot (y + (-1)) \cdot (y + 4 \cdot (-1)) |
-30,238 | \frac{1}{x + (-1)} \cdot (x^2 - 2 \cdot x + 1) = \dfrac{1}{x + (-1)} \cdot (x + \left(-1\right)) \cdot (x + \left(-1\right)) = x + (-1) |
6,055 | xzR \Rightarrow zRx |
9,711 | 720 = 2^4*5*3^2 |
-21,039 | (5*\left(-1\right) + a)/8*\frac{7}{7} = \frac{1}{56}*\left(7*a + 35*(-1)\right) |
2,014 | (-z + y) (y + z) (z^2 + y^2) = y^4 - z^4 |
9,079 | 71 + 5*(n + 13*(-1)) = n*5 + 6 |
-3,407 | -\sqrt{11} + \sqrt{11}\cdot 3 = -\sqrt{11} + \sqrt{11} \sqrt{9} |
-20,218 | \frac{1}{5p + 8\left(-1\right)}(\left(-1\right) - p \cdot 5) \cdot 7/7 = \frac{7\left(-1\right) - p \cdot 35}{56 (-1) + 35 p} |
17,440 | \left(e^x\right)^2 = e^{2 \cdot x} |
-24,649 | 3/12 = -\dfrac13*2 + 3/4 + 1/6 |
1,444 | 12 = C_3*3 \implies C_3 = 4 |
12,552 | y^2 = (y + 0\cdot (-1))\cdot (0\cdot (-1) + y) |
34,321 | (z + I)\cdot (z + 1 + I) = z^2 + z + I = z^2 + 1 + z + \left(-1\right) + I = z + 1 + I |
5,388 | 3/(2*y) + 1/2 = \tfrac{1}{y*2}*\left(y + 3\right) |
20,266 | 1^r=\frac{1^r}{1^r} |
27,483 | 1 - 25/36 = \frac{1}{36}\cdot 11 |
28,990 | \frac{1}{i!\cdot (n - i)!}\cdot n! = {n \choose i} |
6,250 | \mathbb{E}[D_2]\cdot \mathbb{E}[D_1] = \mathbb{E}[D_2\cdot D_1] |
2,403 | (d + 2)^2 = d^2 + 4 + 4 \cdot d |
644 | \frac{\partial}{\partial z} \left(a*z^n\right) = a*\frac{\partial}{\partial z} z^n = a*n*z^{n + (-1)} |
-2,831 | \sqrt{2} \cdot \sqrt{9} - \sqrt{2} = -\sqrt{2} + \sqrt{2} \cdot 3 |
31,895 | \cos(2\cdot z) = \cos^2(z)\cdot 2 + (-1) |
-4,176 | x^4 \cdot 2 = x^4 \cdot 2 |
8,716 | \sin\left(x_2 + x_1\right) = \cos{x_2}*\sin{x_1} + \sin{x_2}*\cos{x_1} |
2,036 | \frac{\partial}{\partial x} (8*s*x) = 8*s*\frac{\mathrm{d}x}{\mathrm{d}x} + 8*\frac{\mathrm{d}s}{\mathrm{d}x}*x |
10,938 | (z + 1)^2 = (z + 4 + 3\cdot \left(-1\right)) \cdot (z + 4 + 3\cdot \left(-1\right)) = \left(z + 4\right)^2 - 6\cdot (z + 4) + 9 |
-30,839 | 312.5 = \frac{25^2}{2} |
16,265 | \operatorname{acos}\left(\frac12\right) = \pi/3 |
-20,214 | 4/4 \cdot (-\dfrac{2}{-x \cdot 7 + 6 \cdot (-1)}) = -\frac{8}{-x \cdot 28 + 24 \cdot (-1)} |
-10,773 | \frac{10 (-1) + x*40}{x*50 + 20} = \frac{10}{10} \frac{\left(-1\right) + 4 x}{2 + 5 x} |
44,310 | {8 \choose 2} = {\left(-1\right) + 6 + 3 \choose \left(-1\right) + 3} |
13,091 | \tan{\chi} = \frac{\sin{\chi}}{\cos{\chi}} |
23,231 | \frac{a}{b} = 1/(\frac1a*b) |
21,540 | 0.25 = (0.5 - 0.25) |
-26,083 | \dfrac{-2 + i}{-2 + i} \dfrac{1}{-2 - i}(i*8 + 1) = \frac{8i + 1}{-2 - i} |
-9,623 | 0.01 (-96) = -\dfrac{96}{100} = -24/25 |
14,599 | (n^4*2 - 2*n^2 + 1) * (n^4*2 - 2*n^2 + 1) + \left(n^5 - 2*n^2 * n + 2*n\right)^2 = n^{10} + 1 |
20,941 | (x + \left(-1\right)) \cdot (x + \left(-1\right)) + 1 = 2 + x^2 - 2x |
23,288 | 1 + \tfrac{1}{\frac{1}{1^{-1} + 1} + 1} = \frac53 |
20,031 | 5y = (q*5 + 1)*19 + 1\Longrightarrow y = q*19 + 4 |
47,671 | 71.5 = \frac{1}{2}*13*11 |
2,336 | 10/24 = \dfrac{1}{24}*(6 + 4) |
9,935 | {n \choose m}/n = \dfrac{1}{m! \cdot (n - m)!} \cdot (n + (-1))! = \tfrac{1}{m} \cdot {n + \left(-1\right) \choose m + \left(-1\right)} |
18,749 | b\cdot D/b\cdot b = D\cdot b |
13,244 | \frac{19!}{24!}\cdot 22!\cdot 1/17! = \frac{18\cdot 19}{23\cdot 24} = 0.6196 |
-7,108 | \frac{6}{14}\cdot 6/15 = 6/35 |
16,179 | 2 - \frac{1}{w + \left(-1\right)}\cdot w = \frac{1}{w + \left(-1\right)}\cdot \left(2\cdot w + 2\cdot (-1) - w\right) = \frac{1}{w + (-1)}\cdot \left(w + 2\cdot (-1)\right) |
11,786 | \sin\left(\arcsin(y)\right) = y |
8,067 | 4 \cdot p \cdot q \cdot r + p^3 + q^3 + r^3 = -3 \cdot q \cdot r \cdot (r + q) + p^3 + (r + q) \cdot (r + q)^2 + 4 \cdot p \cdot r \cdot q |
35,210 | n - i = 1\Longrightarrow i = (-1) + n |
29,046 | \frac{0.6\cdot 0.3}{0.3\cdot 0.6}\cdot 0.3 = 0.3 |
34,972 | \sqrt{3} \cdot 2 + 3 \cdot \left(-1\right) = -3 + 2 \cdot \sqrt{3} |
-9,638 | 12\% = 12/100 = 3/25 |
15,938 | \cos{2\cdot \theta} = 1 - 2\cdot \sin^2{\theta} |
10,218 | \left(y \times y \times 3 = y^4 \Leftrightarrow 1 + y^2 = \left(y^2 + (-1)\right)^2\right) \Rightarrow 3^{1 / 2} = y |
-15,659 | \frac{1}{q^4\cdot \dfrac{1}{q^{20}\cdot \dfrac{1}{x^5}}} = \tfrac{1}{q^4\cdot \frac{1}{q^{20}}\cdot x^5} |
34,740 | \frac{4 \cdot {9 \choose 5}}{{52 \choose 5}} \cdot 1 = 3/15470 |
-7,652 | \frac{5i + 5}{-1 - 2i} = \frac{1}{-1 + i*2}(-1 + i*2) \dfrac{i*5 + 5}{-1 - i*2} |
-4,561 | (2 + z) \cdot \left(z + 3 \cdot \left(-1\right)\right) = z^2 - z + 6 \cdot (-1) |
-20,189 | \dfrac44\cdot (-\frac{2}{x + 1}) = -\frac{8}{x\cdot 4 + 4} |
30,006 | (2 \cdot 3^x)^2 = 3^{2 \cdot x} + 3^{x \cdot 2 + 1} |
-7,392 | 3/8 = 1/4\cdot 3/2 |
14,418 | 27^{\frac23} = (27^{1/3})^2 = 3^2 = 9 |
5,651 | \sqrt{\frac{a^3b}{c^4}}=\frac{a^{3/2}b^{1/2}}{c^2}=a^{3/2}b^{1/2}c^{-2} |
35,204 | 43^2 = 1 + 24\cdot 77 |
37,570 | 49 * 49^2 = 343^2 = 117649 |
11,208 | \left(\sin{\pi} \cdot i + \cos{\pi}\right) = -1 |
1,909 | 3 \cdot \left(k + 1\right) \cdot \left(k + 1\right) = 4 \cdot k + 3 + k^2 \cdot 3 - 1 + 2 \cdot k + k \cdot 4 + 1 |
-20,837 | -3/4*\dfrac{x + 9}{9 + x} = \frac{1}{x*4 + 36}*(-3*x + 27*(-1)) |
37,372 | 2^m = (2 + 1)^2 + (-1) = 2^3 \Rightarrow m = 3 |
12,099 | N \cdot 2 - 2 \cdot N^5 = 0 rightarrow (-N^4 + 1) \cdot N = 0 |
30,892 | \left(2^{10500}\right)^{1/2} = 2^{\frac{1}{2}\cdot 10500} = 2^{5250} |
-4,770 | \tfrac{3}{\left(-1\right) + x} + \tfrac{1}{x + 4 \cdot \left(-1\right)} \cdot 3 = \frac{1}{x^2 - x \cdot 5 + 4} \cdot \left(15 \cdot (-1) + 6 \cdot x\right) |
23,995 | \int\limits_c^f k\,\mathrm{d}x = \int\limits_c^f k\,\mathrm{d}x |
-10,781 | -\frac{12}{50\cdot q + 40\cdot (-1)} = \frac22\cdot (-\dfrac{1}{q\cdot 25 + 20\cdot (-1)}\cdot 6) |
10,940 | \frac{1}{\sqrt{n}} (-n + 2 X_n) = (-\frac{n}{2} + X_n)/(\sqrt{n} \dfrac{1}{2}) |
-25,026 | -\frac{1}{-z + 1} = -1 - z - z \cdot z - z \cdot z \cdot z - z^4 - \ldots |
12,700 | 16^l + 16 \cdot \left(-1\right) = 16 \cdot \left((-1) + 16^{(-1) + l}\right) |
-18,497 | -37/35 = -\frac{1}{35}37 |
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