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7,008 | {3 \choose 2}*{7 + 6*(-1) + (-1) \choose (-1) + 3} = 0 |
16,271 | 2^{c b} + (-1) = (2^c)^b + (-1) = \left(2^c + (-1)\right) ((2^c)^{b + (-1)} + (2^c)^{b + (-1)} + \dots + 1) |
2,162 | \tfrac{1}{4}\cdot \left(600 - 6\cdot z\right) = -z\cdot \frac12\cdot 3 + 150 |
1,983 | (a^4)^{\frac15} (a^6)^{\dfrac15} = a^{\frac{4}{5}} a^{\frac{6}{5}} = a^2 |
10,900 | N \cdot m_2 \cdot N \cdot m_1 = N \cdot m_1 \cdot m_2 \cdot N |
-25,371 | \tan{d} = \frac{\sin{d}}{\cos{d}} |
22,313 | a*h*e + a'*e + x*a' + e*h = e*h*a + a'*e + a'*x |
-5,044 | 1.08*10 = \frac{1.08*10}{1000} = 1.08/100 |
25,302 | 6 \cdot h^2 = 4 \cdot h^2 + 2 \cdot h_2 \cdot h_3 = \left(h_2 + h_3\right) \cdot \left(h_2 + h_3\right) + 2 \cdot h_2 \cdot h_3 |
1,381 | A*\dots*A/l = A^l |
18,744 | x^4 - x^2 + 1 = (x^2 - \frac12)^2 + \tfrac34 |
2,868 | x^2 + 4 \cdot (-1) = \left(x + 2 \cdot (-1)\right) \cdot (2 + x) |
10,779 | d^3 + f^3 = (d + f)\cdot (d^2 - d\cdot f + f^2) |
-1,260 | -\dfrac{1}{18}\cdot 20 = \frac{\left(-20\right)\cdot 1/2}{18\cdot \dfrac12} = -\dfrac{1}{9}\cdot 10 |
33,787 | \varphi^5 = -\bar{\varphi} = -\frac{1}{\varphi} |
19,215 | x^{\dfrac1s} = x^{1/s} |
37,763 | 7^8 - 7^6 + 7^4 - 7^2 + 1 = 5649505 = 5*281*4021 |
-21,042 | 2/10\times 10/10 = 20/100 |
-8,087 | \frac{1}{34}*(6 - 24*i - 10*i + 40*(-1)) = (-34 - 34*i)/34 = -1 - i |
19,563 | (a - x) (x^2 + a^2 + xa) = -x^3 + a^3 |
-7,249 | 1/120 = \frac{2\cdot \dfrac{1}{9}}{8}\cdot 10^{-1}\cdot 3 |
29,837 | c_1 ( 1, 0) + x\cdot ( 1, 1) = ( c_1 + x, x) = \left\{0\right\}\Longrightarrow c_1 = x = 0 |
-4,684 | \dfrac{5}{5 + x} + \frac{1}{x + 1} \cdot 5 = \frac{x \cdot 10 + 30}{x \cdot x + x \cdot 6 + 5} |
-3,656 | \dfrac{63}{70 \cdot q^4} \cdot q = \dfrac{63}{70} \cdot \frac{q}{q^4} |
8,285 | e\cdot h := e\cdot h |
24,416 | \pi = 3.14159265358 \cdot \cdots = 3 + 1/10 + 4/100 + \dfrac{1}{1000} + \tfrac{5}{10000} + \cdots |
-519 | e^{14*\frac{i*\pi*4}{3}} = (e^{\frac{i*\pi*4}{3}*1})^{14} |
37,388 | 2^3*5*17 = 680 |
-20,676 | \frac{1}{r \cdot (-42)} \cdot \left(14 \cdot (-1) + r \cdot 7\right) = 7/7 \cdot \dfrac{2 \cdot (-1) + r}{(-6) \cdot r} |
3,707 | x \cdot m_1 + t_1 = y \cdot m_2 + t_2 rightarrow m_1 \cdot x - y \cdot m_2 = -t_1 + t_2 |
39,716 | dx = dx |
18,549 | 2000 = 4\cdot 4\cdot 5 \cdot 5 \cdot 5 |
8,585 | d_1 \cdot d_2 = \dfrac{1}{d_1 \cdot d_2} = \dfrac{1}{d_2 \cdot d_1} = d_2 \cdot d_1 |
50,750 | (-1)\times 9 = -9 |
1,996 | \frac12 \cdot z = \delta \Rightarrow 0 \leq \delta = \frac{z}{2} \lt z |
3,761 | z \cdot z + 3 \cdot z = (3/2 + z)^2 - \tfrac94 |
18,769 | 6^x = 36\cdot 9.75^{x + 2 (-1)}\cdot 6^x = 6^2 (9 + 3/4)^{x + 2 (-1)} |
-7,549 | \frac{1}{26} \cdot (-7 - 9 \cdot i + 35 \cdot i + 45 \cdot (-1)) = \left(-52 + 26 \cdot i\right)/26 = -2 + i |
37,796 | \mathbb{E}[U_1 \cdot U_2] = \mathbb{E}[U_2] \cdot \mathbb{E}[U_1] |
16,388 | (x + y)*z = \left(x + y\right)*(z + 0) = x*z + y*z |
-3,250 | -\sqrt{8} + \sqrt{18} = -\sqrt{4\cdot 2} + \sqrt{9\cdot 2} |
6,998 | n \geq 15\Longrightarrow n \cdot 14/15 + 1 \leq n |
9,620 | 4 + 4 \cdot n \cdot n + 8 \cdot n = (1 + n)^2 \cdot 4 |
5,077 | \sin{\tfrac{x}{2}} = \cos{x/2} = \sin(\frac{\pi}{2} - x/2) |
16,326 | \chi = (\chi - \alpha Z) (\chi - 0.4 Z) = \chi - (0.4 + \alpha - 0.4 \alpha) Z |
47,526 | 10000 - 100 = 9900 |
-23,162 | -1/4 = \frac{1}{2} \cdot \left(1/2 \cdot (-1)\right) |
12,970 | 4/27 = 1/3*2/3*2/3 |
6,377 | 0 = \sqrt{30 + 5\cdot \left(-1\right)} + 5 \Rightarrow 5 + 5 = 10 \neq 0 |
14,450 | 12^{1 / 2} = \left(4 \cdot 3\right)^{1 / 2} = 4^{\frac{1}{2}} \cdot 3^{1 / 2} = 2 \cdot 3^{1 / 2} |
10,538 | (1 + x)^{(-1) + k}\cdot (1 + x) = (1 + x)^k |
-10,504 | \dfrac{1}{4}*4*(-\frac{1}{n^2}) = -\dfrac{1}{n^2*4}*4 |
-15,299 | \frac{k^3}{\frac1k \frac{1}{p^5}} = \frac{k^3}{\frac{1}{p^5}\cdot 1/k} |
31,956 | 1 + x^6 = (x^2 + 1) \cdot (1 - x \cdot 3^{\frac{1}{2}} + x^2) \cdot (x^2 + 1 + 3^{\frac{1}{2}} \cdot x) |
134 | \mathbb{E}(X \cdot Z) = \mathbb{E}(Z) \cdot \mathbb{E}(X) |
615 | \frac{y x}{r^2} 2 = \frac{y}{r} \cdot 2 x/r |
14,441 | q^{h + c} = q^c\cdot q^h |
-25,368 | d/dx (\frac{1}{x^2} \cdot \sin{x}) = \dfrac{1}{x^3} \cdot (-\sin{x} \cdot 2 + \cos{x} \cdot x) |
17,594 | 7/z = 1/12 rightarrow 84 = z |
-7,682 | \frac{1}{5}\cdot \left(4 - 18\cdot i - 2\cdot i + 9\cdot (-1)\right) = \left(-5 - 20\cdot i\right)/5 = -1 - 4\cdot i |
42,984 | \frac{1}{\sqrt{f}} = \frac{\sqrt{f}}{\sqrt{f}}\cdot 1/(\sqrt{f}) = \frac{1}{f}\cdot \sqrt{f} |
41,122 | 5/100 = \tfrac{1}{20} |
26,483 | 2\cdot y - y^2 = -((-1) + y)^2 + 1 \implies \left(-y^2 + 2\cdot y\right)^{\frac{1}{2}} = (1 - ((-1) + y)^2)^{1 / 2} |
3,825 | x^{l + 1} = x^l\cdot x \leq x^l |
29,189 | \sqrt{x^6} = |x \cdot x \cdot x| = -x^3 |
-4,524 | (3 + z) \left(1 + z\right) = z^2 + 4 z + 3 |
40,048 | -1 = 0 * 0 - 1^2 |
36,927 | 1/\left(y*z\right) = \dfrac{1}{y*z} |
-15,210 | \dfrac{1}{\frac{1}{t^{20}}*\frac{1}{\frac{1}{p}*t * t}} = \frac{t^{20}}{\frac{1}{t^2}*p} |
25,818 | \overline{y_2 + y_1} = \overline{y_2} + \overline{y_1} |
23,081 | 29^{1/2} = 5 + \frac{1}{1} \cdot (29^{1/2} + 5 \cdot (-1)) |
10,360 | (\sqrt{2} + 5) \times (-\sqrt{2} + 2) = (-\sqrt{2} \times 7 + 11) \times (2 + \sqrt{2}) |
3,181 | n^3*(n^3 + 1)*\left(n^3 + (-1)\right) = n^9 - n^3 |
23,810 | \tanh{x} = \frac{\sinh{x}}{\cosh{x}} = \frac{1}{1 + e^{-2 \cdot x}} \cdot (1 - e^{-2 \cdot x}) |
35,022 | d/h = \frac{d}{h} |
-22,872 | \dfrac{13\cdot 8}{7\cdot 13} = 104/91 |
28,230 | m + 1 + n + 1 = n + 1 + m + 1 |
38,059 | 3 + 1 + 1 + 2 = 8 + (-1) |
15,875 | -i = 0 - i = \cos(3\times \pi/2) + \sin(3\times \pi/2)\times i |
-29,668 | \frac{d}{dz} (-2 \cdot z^5) = -2 \cdot d/dz z^5 = -2 \cdot 5 \cdot z^4 = -10 \cdot z^4 |
20,463 | -\frac{1}{y^2} = \frac{\mathrm{d}}{\mathrm{d}y} \frac1y |
31,046 | det\left(A_1 \cdot \cdots \cdot A_l\right) = det\left(A_1\right) \cdot \cdots \cdot det\left(A_l\right) |
1,234 | \alpha, \beta, \beta \geq \alpha \Rightarrow \beta = \beta \times \alpha |
8,750 | (l + 1) * (l + 1) - l * l = l * l + 2l + 1 - l^2 = 2l + 1 |
-17,672 | 39 = 34 \cdot (-1) + 73 |
2,119 | \cos(2014*\pi/12) = \cos(-83*2*\pi + \frac{2014*\pi}{12}) |
13,603 | a = c = \tfrac{1}{2}\cdot \left(a + c\right) |
14,079 | \left(b^2 + a^2\right)^2 = (a^2 - b \cdot b)^2 + (b\cdot a\cdot 2)^2 |
10,950 | \tfrac{x}{2} \cdot (x + (-1)) = {x \choose 2} |
24,563 | \frac{1}{\cosh\left(z\right)} \times \sinh(z) = \tanh(z) |
5,234 | 1 + \left(2^k + (-1)\right) \cdot 2 = 2^{k + 1} + (-1) |
28,435 | \arctan{\tfrac{1}{1 + 3/4\cdot 5/12}\cdot (-5/12 + \dfrac{1}{4}\cdot 3)} = \arctan{16/63} |
-6,305 | \frac{1}{(9 (-1) + y) (6 + y)} = \dfrac{1}{54 \left(-1\right) + y^2 - 3 y} |
4,379 | x\cdot \Delta\cdot g = \Delta\cdot g\cdot x |
20,480 | \dfrac{5}{1 + n} = \frac{1}{5^n}n! \frac{5^{1 + n}}{\left(n + 1\right)!} |
18,956 | (f \cdot f + x^2 + f \cdot x) \cdot \left(x - f\right) = -f \cdot f \cdot f + x^3 |
28,097 | (c^{1/2} - f^{1/2}) \cdot (c^{1/2} + f^{1/2}) = c - f |
15,649 | 3f = x + 2(f + \left(-1\right))\Longrightarrow x = 2 + f |
24,770 | (y^2 + y*2 + 2)*(y^2 - y*2 + 2) = y^4 + 4 |
2,773 | k*4 + 1 + l*4 + 1 = 2 + \left(k + l\right)*4 |
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