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33,360 | |a - z|^2 = \sqrt{(a - z)\cdot \overline{a - z}} \cdot \sqrt{(a - z)\cdot \overline{a - z}} = (a - z)\cdot \overline{a - z} |
-15,932 | -6/10 + 7\cdot 9/10 = \tfrac{1}{10}\cdot 57 |
7,342 | \dfrac{1}{(-1) + z} \cdot (z + \left(-1\right)) \cdot (1 + z) = \frac{z^2 + (-1)}{z + \left(-1\right)} |
-4,904 | 1.5*10^{\left(-5\right) (-1) - 5} = 1.5*10^0 |
5,994 | G = G^{\frac{1}{2}} G^{1/2} |
32,835 | 1587/12167 = \frac{3}{23} |
33,018 | 0 = t^i*b^i = (t*b)^i |
30,545 | \frac{1 + 2}{2 + 4} = 0.5 |
-14,312 | 8 + 10 \cdot \frac11 \cdot 7 = 8 + 10 \cdot 7 = 8 + 10 \cdot 7 = 8 + 70 = 78 |
11,532 | f = e \times \frac{f}{e} |
-10,768 | \dfrac{50}{s\cdot 15 + 60} = \dfrac{10}{12 + s\cdot 3}\cdot 5/5 |
38,374 | 162 \cdot \left(-1\right) + 48 + 24 + 72 \cdot (-1) + 162 = 0 |
1,147 | \tan{x} + \left(-1\right) = \frac{1}{\cos{x}} \cdot \sin{x} + (-1) = \dfrac{1}{\cos{x}} \cdot (\sin{x} - \cos{x}) |
17,523 | (2 + 1) (7 + 1)/6 = (1 + 1) \cdot (1 + 1) |
-3,210 | 3^{1/2}*(3*(-1) + 2 + 5) = 3^{1/2}*4 |
-4,614 | \frac{9*x + 13*(-1)}{x^2 - x*3 + 2} = \frac{4}{(-1) + x} + \frac{5}{2*(-1) + x} |
34,782 | 1 + 2^{3^{l + 1}} = (2^{3^l})^3 + 1 |
-540 | \dfrac{1}{6} \cdot 11 \cdot \pi = \tfrac{95}{6} \cdot \pi - \pi \cdot 14 |
21,755 | a^3 - b * b * b = \left(a - b\right)*(a * a + a*b + b * b) |
1,597 | (4-1)^2 + (3+4/3)^2 = 27.77...\neq 25 |
-10,920 | \dfrac{1}{6}\cdot 66 = 11 |
3,108 | \frac{1}{x\times y} = \frac{1}{x + y}\times \left(1/x + 1/y\right) |
264 | (z + \left(-1\right))\cdot \left(z^6 + z^5 + \cdots + z + 1\right) = z^7 + (-1) |
32,634 | 10\cdot 4\cdot 60 = 2400 |
17,123 | \frac{5}{6} - \tfrac{1}{5} = \frac{1}{30} \cdot 19 |
35,937 | 1 - \sqrt{z^4 - z^2} = \left(z + (-1)\right)^2 = z^2 - 2*z + 1 |
-20,729 | \frac{1}{63 + y\cdot 70}\left(-y\cdot 50 + 45 (-1)\right) = -5/7 \dfrac{9 + 10 y}{10 y + 9} |
9,148 | 0 = A \cdot C - A \cdot C = A \cdot B/k - \frac{1}{m} \cdot B \cdot C = \frac{1}{m \cdot k} \cdot (A \cdot B \cdot m - k \cdot B \cdot C) |
1,614 | \sin(2\cdot x) = \frac{2\cdot \tan(x)}{1 + \tan^2(x)} |
8,467 | -\tfrac{\pi}{8} + \pi \cdot 0 = -\frac{\pi}{8} |
-22,245 | i^2 - i\cdot 17 + 70 = (i + 7\cdot (-1))\cdot (i + 10\cdot (-1)) |
-184 | \binom{8}{4} = \frac{8!}{\left(8 + 4(-1)\right)! \cdot 4!} |
30,239 | x*\tfrac{1}{d}*b = \frac{b*x}{d} |
-1,578 | \frac16*\pi + \pi*11/12 = \frac{13}{12}*\pi |
-6,993 | \tfrac{1}{5}4 \cdot \frac{2}{3} = \frac{8}{15} |
-20,576 | -8/5 \cdot \dfrac{2 \cdot n + 2 \cdot (-1)}{2 \cdot (-1) + 2 \cdot n} = \frac{16 - n \cdot 16}{10 \cdot n + 10 \cdot (-1)} |
26,567 | A \cdot (B + C) = A \cdot B + C \cdot A |
12,884 | {20 \choose 2} = \dfrac{20}{2}\cdot 19 |
-16,427 | 2\sqrt{16*11} = \sqrt{176}*2 |
-17,553 | 84 + 82 \cdot \left(-1\right) = 2 |
-1,364 | 9/2\cdot (-\frac52) = 9\cdot \frac{1}{2}/(\dfrac15\cdot (-2)) |
10,460 | 1 = x + 1/4 + 5/8 \implies 1/8 = x |
14,757 | 134 = (1 + 4 + 14 + 48)\cdot 2 |
-7,118 | \tfrac{1}{9} \cdot 5 \cdot \tfrac17 \cdot 3 = \frac{5}{21} |
43,039 | i \cdot i = ... = 1 |
32,095 | 0 \neq y\Longrightarrow y/y = 1 |
13,802 | \frac{x^2 + 1}{x - i} = \dfrac{1}{x - i} \cdot (x - i) \cdot \left(x + i\right) = x + i |
36,293 | 4*(1 + s^2) = \left(1 + s^2 - s*x\right)^2 + x^2 = (1 + s * s)*(1 + (x - s)^2) |
17,351 | (-1)\cdot (-19) = 19 |
3,431 | 15 = {6 \choose 2}*{1 \choose 1} |
1,445 | j^2 + j + 1 = 0 \Rightarrow j^2 + 1 = -j |
-2,626 | \sqrt{24} - \sqrt{6} = -\sqrt{6} + \sqrt{4*6} |
-24,827 | 4995/5 = 999 |
13,586 | \binom{4}{2} \binom{12}{3} = -\binom{11}{3} + \binom{23}{3} - \binom{13}{3} |
2,804 | t * t^2 - t^2*3 + t + 1 = (t^2 - 2*t + \left(-1\right))*(t + \left(-1\right)) |
29,226 | \dfrac13(\delta + (-1)) + \frac{1}{3}(1 + \delta) = \delta \dfrac{2}{3} |
-29,565 | 4/z + \frac{2z^4}{z}1 + z*5/z = \tfrac1z\left(4 + z^4*2 + 5z\right) |
17,143 | n^2 = n\sum_{j=1}^n 1 = \sum_{j=1}^n n |
25,788 | 41 = 5 * 5 + 4 * 4 |
2,834 | W\cdot t^2 = \left(t\cdot W + q\right)\cdot t = t\cdot (t\cdot W + q) + q\cdot t = t \cdot t\cdot W + 2\cdot t\cdot q |
-16,439 | \sqrt{99}*3 = \sqrt{9*11}*3 |
36,892 | 0.1 \cdots = 0.099 |
9,057 | \frac{1}{1 + f^x}\cdot f^x = \frac{1}{1 + f^x}\cdot (f^x + 1 + (-1)) = 1 - \frac{1}{1 + f^x} |
-25,241 | \frac{\text{d}}{\text{d}x} (x^2)^{1/5} = x \cdot \frac{2}{5} |
21,554 | \frac{1}{1 - q} (q^{1 + m} \left(1 - q\right) + 1 - q^{1 + m}) = 1 + \ldots + q^{1 + m} |
29,200 | p^2\cdot \pi/\pi = p^2 |
5,487 | 1/\left(h_1*h_2\right) = 1/(h_2*h_1) |
33,408 | (2\cdot k + (-1)) \cdot (2\cdot k + (-1)) = 1 + \binom{k}{2}\cdot 8 |
27,898 | \frac{1}{x + 2 \cdot (-1)} \cdot (2^x - x^2) = \dfrac{2^x + 4 \cdot (-1) + 4 - x^2}{x + 2 \cdot (-1)} = 4 \cdot \frac{1}{x + 2 \cdot (-1)} \cdot (2^{x + 2 \cdot (-1)} + \left(-1\right)) - x + 2 |
-20,527 | 56/(-48) = -7/6 \cdot (-\frac{8}{-8}) |
6,321 | \frac{1}{25} = \tfrac{1^{-1}}{\frac{1}{1/25}} |
-18,483 | 4 \cdot t + 2 = 10 \cdot (3 \cdot t + 7 \cdot (-1)) = 30 \cdot t + 70 \cdot (-1) |
45,932 | 525 = {6 \choose 4}\cdot {7 \choose 4} |
3,978 | \frac{2}{13} = \frac{1}{2 + 4 + 7} \cdot 2 |
12,356 | 4^2 + 6 * 6 = 52 |
-24,815 | -2448 = 2445\cdot (-1) - 3 |
2,554 | 10 + z^2 + 7\cdot z = (2 + z)\cdot (5 + z) |
9,411 | \frac{1}{\tan{\theta}} = \frac{1}{\sin{\theta} \frac{1}{\cos{\theta}}} |
1,467 | \left(12 + 16\right) \cdot 3/7 = (12 + 30) \cdot 2/7 |
755 | \|G \cdot x\|^2 - \|A \cdot x\|^2 = \left( G \cdot x, G \cdot x\right) - ( A \cdot x, A \cdot x) = ( G^2 \cdot x, x) - ( A^2 \cdot x, x) = ( (G^2 - A \cdot A) \cdot x, x) |
-26,457 | (\tfrac{24\cdot d}{6} - 18\cdot b/6)\cdot 6 = 6\cdot \left(d\cdot 4 - 3\cdot b\right) |
3,331 | x \cdot \frac{c}{h} = \frac{x}{h} \cdot c |
1,069 | a \neq 0\Longrightarrow 0 \neq a + a |
35,548 | 3 \cdot (-1) + z = v \Rightarrow z = 3 + v |
30,163 | z = a + i \cdot b \implies \bar{z} = a - b \cdot i |
37,199 | p^n = \binom{p^n}{1} |
-564 | e^{i\pi \cdot 15} = (e^{\pi i})^{15} |
-10,711 | -\frac{3}{5 \cdot y + 3} \cdot \frac{1}{6} \cdot 6 = -\frac{18}{18 + 30 \cdot y} |
9,341 | \left(3\cdot (-1) + x\right)^2 - x\cdot 4 = (x + (-1))\cdot (x + 9\cdot (-1)) |
2,845 | \sin{y} = \sin(y - e + e) = \sin(y - e)\cdot \cos{e} + \cos(y - e)\cdot \sin{e} |
7,799 | ∅ = [1,2] = 2\times \left( 1, 1\right) |
29,561 | \dfrac{2}{3\sqrt{3}} = 2\sqrt{3}/9 |
17,570 | \frac{1}{(k + 1) \cdot (k + (-1))} = -\dfrac{\frac12}{k + 1} + \frac{1/2}{\left(-1\right) + k} |
641 | c + 2 \cdot c + 3 \cdot c + 10 = 250 \implies c = 40 |
670 | (a - b) \cdot (a - b) = (a - b) \left(a - b\right) = a^2 - 2ab + b^2 |
17,837 | \frac{1}{(-1) + z^3} = (\frac{1}{z + (-1)} - \frac{z + 2}{1 + z^2 + z})/3 |
17,112 | xy=0=x+y |
-3,055 | 3\sqrt{7} = \sqrt{7}*(2(-1) + 5) |
24,185 | \min{\mathbb{E}(X),\mathbb{E}(Z)} = \mathbb{E}(\min{X,Z}) |
-20,183 | \dfrac{-6}{1} \times \dfrac{-7k + 10}{-7k + 10} = \dfrac{42k - 60}{-7k + 10} |
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