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12,618 | \sqrt{x - g} \dfrac{x - g - x - h}{\left(-h + x\right) (-g + x)} = \dfrac{-g + h}{\sqrt{-g + x} (x - h)} |
4,392 | (a^2 - g^2) \cdot u = (a + g) \cdot (-g + a) \cdot u |
10,543 | x^2 = -(x + 3 \times (-1)) \times (-x + 5) - 4 \times (8 - 2 \times x) + 17 |
8,295 | \left(6 + 20^{1 / 2}\right)^{1 / 2} = \left(5^{1 / 2} \cdot 2 + 6\right)^{\dfrac{1}{2}} |
12,995 | (c - d)^2 = d^2 + c^2 - cd \cdot 2 |
33,375 | (2\cdot (-1) + z\cdot 3)\cdot (5 + z) = 10\cdot (-1) + z^2\cdot 3 + 13\cdot z |
-657 | (e^{\dfrac{7}{4} \cdot i \cdot \pi})^3 = e^{3 \cdot \frac14 \cdot \pi \cdot 7 \cdot i} |
-9,092 | 138\% = \frac{138}{100} |
-7,426 | 9/91 = \frac{6}{14} \cdot \frac{3}{13} |
-6,707 | \frac{1}{100}\cdot 30 + \dfrac{5}{100} = \frac{5}{100} + \frac{3}{10} |
36,087 | 17 + 4 \cdot (-4) = 1 |
-10,385 | \frac{40 + s \cdot 4}{60 \cdot s + 40 \cdot (-1)} = \frac{s + 10}{10 \cdot (-1) + 15 \cdot s} \cdot \frac{1}{4} \cdot 4 |
-7,627 | (-2 + 26 i - i + 13 (-1))/5 = (-15 + 25 i)/5 = -3 + 5i |
31,459 | \int\limits_g^f \cot{z}\,\mathrm{d}z = \int\limits_g^f \cot{z}\,\mathrm{d}z |
21,892 | (2 + (-1) + 2\cdot x + (-1))/2 = x |
23,425 | 2\cdot \sin{u}\cdot \sin{v} = \cos(-u + v) - \cos(v + u) |
36,075 | -\frac{1}{27} = \dfrac{1}{-27} |
7,351 | \mathbb{Var}\left(Q\right) = \mathbb{E}\left((Q - \mathbb{E}\left(Q\right))^2\right) = \mathbb{E}\left(Q^2\right) - \mathbb{E}\left(Q\right)^2 |
-14,002 | 10\cdot 7 + 2\cdot 24/3 = 10\cdot 7 + 2\cdot 8 = 70 + 2\cdot 8 = 70 + 16 = 86 |
24,872 | 3 = y\cdot 4 - 2\cdot (1 - y) \Rightarrow 5/6 = y |
36,721 | \sqrt{f'^2 + f \cdot f} = \sqrt{f^2 + f'^2} |
12,149 | \frac{-x + 1}{3\times (x^2 + 2)} + \frac{1}{3\times \left(1 + x\right)} = \dfrac{1}{(x \times x + 2)\times (x + 1)} |
15,390 | \sqrt{0.5 \cdot 2} = 1 |
-25,807 | \tfrac{2}{7\cdot 6} = 2/42 |
-25,689 | d/dz (\frac{4}{z + 2}) = -\frac{4}{(2 + z)^2} |
-11,563 | -4 + 15 (-1) + i*4 = i*4 - 19 |
-18,358 | \dfrac{(6*(-1) + t)*t}{(1 + t)*\left(t + 6*(-1)\right)} = \frac{-t*6 + t^2}{t^2 - 5*t + 6*\left(-1\right)} |
-18,403 | \frac{f^2 + f}{f^2 - 3*f + 4*(-1)} = \tfrac{1}{(f + 1)*(f + 4*(-1))}*f*(1 + f) |
-22,315 | (9 + s)\cdot (4 + s) = s^2 + s\cdot 13 + 36 |
-6,049 | \frac{y\cdot 8}{8\cdot (y + 6\cdot (-1))\cdot (y + 9\cdot (-1))} = \frac{y}{(6\cdot (-1) + y)\cdot (y + 9\cdot (-1))}\cdot \frac{1}{8}\cdot 8 |
33,138 | D_x\cdot D_i = D_x\cdot D_i |
53,788 | \frac{(n-1)^{n-1}}{n^{n-2}} = (n-1)\left(1-\frac{1}{n}\right)^{n-2} = (n-1)\left(1-\frac{1}{n}\right)^n \left(1-\frac{1}{n}\right)^{-2} \\ = \frac{n^2}{n-1} \left(1-\frac{1}{n}\right)^n |
2,974 | (1 + 6)\times (4 + 1)\times (2 + 1) = 105 |
-1,715 | \pi*5/6 + \pi \tfrac134 = \pi*13/6 |
8,189 | 1 = z^3 + z - y^2 \implies z^3 + z + (-1) = y * y |
6,658 | (-1) + 2 \cdot \cos^2{Z} = \cos{2 \cdot Z} |
16,784 | I' + I*\lambda = \left(I' + \lambda*I\right)^2 |
4,828 | -\frac{\pi}{4} \cdot 7 = -\dfrac{\pi}{2} \cdot 3 - \frac{1}{4} \cdot \pi |
8,189 | z^3 + z - y \cdot y = 1 \Rightarrow (-1) + z^3 + z = y^2 |
32,915 | \eta^z + \left(-1\right) = (\eta + (-1))\times (\eta^{(-1) + z} + \eta^{2\times (-1) + z} + ... + \eta + 1) |
-17,142 | 2 = 2\cdot 2\cdot q + 2\cdot (-6) = 4\cdot q - 12 = 4\cdot q + 12\cdot (-1) |
25,426 | (1 + n)^4 = 1 + n^4 + n * n^2*4 + 6n * n + n*4 |
587 | \cot{y} - 8 \cdot \cot{8 \cdot y} = \cot{y} - 8 \cdot \cot{8 \cdot y} = \cot{y} - 8 \cdot \dfrac{1}{2 \cdot \cot{4 \cdot y}} \cdot (\cot^{24}{y} + (-1)) |
-16,624 | 8 = 8\cdot (-5\cdot t) + 8\cdot (-1) = -40\cdot t - 8 = -40\cdot t + 8\cdot (-1) |
3,329 | 10^{n + m} = 10^n \cdot 10^m |
17,710 | |c h| = |c| |h| |
16,299 | x_1 + x_2 + v_1 + v_2 = v_2 + x_2 + v_1 + x_1 |
3,670 | \binom{4}{2} = \tfrac{4!}{2!*(4 + 2*(-1))!} = 6 |
23,089 | 2^{1 + k} - 1 + 2^k + 1 = 2^k |
7,858 | (t + t_2 + t_1)^2 - t^2 + t_2^2 + t_1^2 = 2\cdot (t_2\cdot t_1 + t\cdot t_1 + t\cdot t_2) |
21,772 | \frac{xg}{hf}1 = \dfrac{\dfrac1h g}{1/x f}1 |
13,052 | \frac{5}{13} = (10*9 + 2*10)/(\binom{13}{3}) |
28,002 | y = z + 2 \Rightarrow y + 2 \left(-1\right) = z |
2,223 | -(4 + 1 + 2 + 3) = 16 \cdot (-1) + 1 + 4 \cdot (-1) + 9 |
-22,153 | 30/50 = \dfrac15\cdot 3 |
17,559 | 2^{k + 3} + 2^{2 + k} + 2^{1 + k} + 2^k + 2^k = 2^{k + 4} |
9,215 | 1 + \frac{1}{k \cdot k} - 2/k = (1 - 1/k) \cdot (1 - 1/k) |
11,422 | 3 \cdot \left(5 \cdot (-1) + 2 \cdot y\right)^2 \cdot 2 = \left(2 \cdot y + 5 \cdot \left(-1\right)\right) \cdot \left(2 \cdot y + 5 \cdot \left(-1\right)\right) \cdot 6 |
6,924 | l_k\times p_k = l_k\times p_k |
-2,313 | \dfrac{8}{19} - \dfrac{2}{19} = \dfrac{6}{19} |
36,915 | \alpha_x = \alpha_x |
13,049 | -4\cdot (1 + z^2) + 4 = -4\cdot z^2 |
3,942 | |z_2 + z_1 + \varphi| = |z_2 + z_1 + \varphi| |
-5,491 | \frac{z*2}{(z + 1) (z + 2(-1))} = \frac{2z}{z^2 - z + 2(-1)} |
7,847 | 7(-100) + 11 \cdot 67 = 37 |
-30,291 | \tfrac12\cdot (0 + 4) = 4/2 = 2 |
-12,810 | 7 = 15 + 8 (-1) |
39,283 | 3*(12 + 6 (-1)) = 18 |
-7,618 | \frac{-6 + i\cdot 8}{-1 - 2\cdot i} = \tfrac{-1 + 2\cdot i}{-1 + i\cdot 2}\cdot \frac{i\cdot 8 - 6}{-2\cdot i - 1} |
11,449 | -\sin{π/6} - -\sin{\frac56\cdot π} = 0 |
-11,999 | 4/15 = \frac{s}{6\pi}*6\pi = s |
24,838 | \mathbb{E}[Y \cdot V] = \mathbb{E}[Y] \cdot \mathbb{E}[V] |
15,441 | z^{50} = z^{16} \cdot z^2 \cdot z^{32} |
31,468 | e^{-i y} = \cos(-y) + i \sin(-y) = \cos(y) - i \sin(y) |
25,876 | -\left(2 (-1) + x_n^2\right)/(x_n*2) + x_n = \frac12 \left(x_n + 2/\left(x_n\right)\right) |
-9,925 | 0.82 = 8.2/10 = \dfrac{1}{50} \cdot 41 |
11,396 | 20/4 = 2^1*5/2 |
21,075 | \frac{8}{24} - 21/24 = \left(8 + 21\times (-1)\right)/24 = -13/24 |
19,134 | 280 = (20 \cdot \left(-1\right) + 120) \cdot 3 + 20 \cdot (-1) |
4,552 | \dfrac{1}{x^3}(x^3 - 7x) = 1 - \frac{7}{x \cdot x} |
31,466 | 2 + \sqrt{3} = e^{-i*x} = \cos(x) - i*\sin(x) |
55,574 | 10 = \binom{5}{3} |
-22,804 | \frac{54}{4 \cdot 18} \cdot 1 = 54/72 |
34,545 | \dfrac{p}{n} \cdot \tfrac{p + \left(-1\right)}{n + (-1)} = \tfrac{1}{-n + n^2} \cdot (p^2 - p) |
-22,199 | (9 \cdot (-1) + q) \cdot (6 + q) = q \cdot q - q \cdot 3 + 54 \cdot (-1) |
18,918 | \frac{z^2}{z^2 + (-1)}*2 = 2 + \dfrac{1}{z^2 + (-1)}*(z + 1 - z + (-1)) = 2 + \frac{1}{z + (-1)} - \dfrac{1}{z + 1} |
1,704 | u \cdot D^1 = D^{\frac12} \cdot u \cdot D^{\dfrac{1}{2}} |
-6,689 | 0/100 + \frac{1}{100}*7 = 0/10 + \frac{1}{100}*7 |
16,162 | \frac{42}{2}1 + 14 \left(-1\right) = 7 < 14 |
10,012 | \dfrac{x^{4i}}{A_i^4} = x^l \Rightarrow x^{i\cdot 4 - l} = A_i^4 |
-11,595 | -2 + 4 - 9*i = 2 - 9*i |
-17,837 | 8\left(-1\right) + 39 = 31 |
-11,611 | -12 + 12 i = 0 + 12 (-1) + 12 i |
-3,810 | 2\times 3\times 7 = 42 |
26,721 | 13/27 = \frac{1}{3} + \dfrac{2}{9} \cdot 2/3 |
-11,794 | \frac{1}{16} \cdot 9 = \left(3/4\right)^2 |
51,352 | \lim_{n \to \infty} \|\frac{\left(n + 1\right)!}{(n + 1)^{n + 1}} n^n/n!\| = \lim_{n \to \infty} \|\frac{\left(n + 1\right) n!}{(n + 1)^{n + 1}} n^n/n!\| = \lim_{n \to \infty} \|\frac{n + 1}{\left(n + 1\right)^{n + 1}} n^n\| |
53,756 | 2^{2012} = (2^4)^{503} = (-1 + 17)^{503} |
-1,247 | \dfrac{30}{35} = \dfrac{30 \times 1/5}{35 \times \frac{1}{5}} = 6/7 |
29,554 | 3^{n + 1} \gt 3n = n + 2n > n + 1 |
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