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-23,553 | \frac{1}{15}*4 = \frac{1}{3}*2*\frac25 |
4,186 | K_k \cdot K_l = K_l \cdot K_k |
-24,681 | -30 i + 52 \left(-30 i\right) = -30 i + 52 \left(-30 i\right) = 52 (-30 i \cdot (-30 i)) = 52 (-60 i) |
489 | x^{17} = x^5 \cdot x^3 \cdot x^4 \cdot x^5 |
31,139 | 2\cdot \pi\cdot 1/3/(2\cdot \pi) = \frac13 |
-9,156 | -b*7*7 b + b*2*5*7 = -b^2*49 + b*70 |
16,593 | -x^2 + h^2 + f^2 = -2\cdot (f - x)\cdot (h - x) + (h + f - x)^2 |
5,807 | \int_2^3 \dfrac{1}{u}\,du = \int\limits_2^3 \dfrac{1}{x \cdot u} \cdot x\,du |
8,250 | \tanh(x) = \tanh(z) \Rightarrow x = z |
-27,869 | d/dx (-5\times \cot(x)) = -5\times d/dx \cot(x) = 5\times \csc^2\left(x\right) |
2,633 | 0 \cdot z = (z + 1) \cdot 0 |
2,149 | (L^{1/m} - x)^m \lt (L^{\dfrac1m})^m = L < (L^{1/m} + x)^m |
37,186 | \int \sin\left(z\right)\,dz = -\cos(z) |
29,890 | \frac{1}{(z + \left(-1\right))^2} \cdot (z + (-1)) = \dfrac{1}{(-1) + z} |
36,439 | {10 + 4 + (-1) \choose 10} = 286 |
9,556 | \mathbb{E}(|X|) + \mathbb{E}(|Y|) = \mathbb{E}(|Y| + |X|) |
19,639 | Y = a + a^2 + a \cdot a \cdot a + ... \Rightarrow Y - a = a\cdot Y |
721 | 1 = \frac12 + \frac14 + 1/8 + 1/16 + 1/16 |
28,418 | \frac{1}{g} \cdot N = \frac1g \cdot N |
22,913 | b^k = ((b^{\frac{1}{s}})^s)^k = \left(b^{1/s}\right)^{s k} |
6,443 | c - d + h - b \coloneqq h + c - b + d |
-20,116 | p*14/(2*p) = \frac{2*p}{2*p}*\frac71 |
-18,384 | \dfrac{t^2 - 8t}{24 (-1) + t \cdot t - t \cdot 5} = \frac{t}{(3 + t) (t + 8\left(-1\right))}(8(-1) + t) |
47,485 | \dfrac{1}{1 - z} = \tfrac{1}{1 - w - z - w} = \frac{1}{(1 - w)\cdot (1 - \tfrac{1}{1 - w}\cdot \left(z - w\right))} |
26,098 | 4\pi - 3\pi = \pi |
24,123 | d/dx e^{-2\times x} = -2\times e^{-x\times 2} |
16,108 | \frac{n \times l}{x \times j} = \dfrac{n \times 1/x}{\dfrac{1}{l} \times j} |
39,815 | 5*2 + 10*2 + 20*2 + 30 + 30*2 + 20 = 180 |
14,263 | n*m*2 = 6 \implies 3 = n*m |
30,003 | 19 \cdot (-1) + 35 = 16 |
-29,372 | (y + 2) (y + 5) = y * y + 5y + 2y + 10 = y * y + 7y + 10 |
10,258 | (i - l)\cdot (l - i) = l\cdot (i - l) - i\cdot (i - l) |
14,099 | e + d = d - -e |
12,894 | 2 \cdot 7/6 \cdot (12 + 9 \cdot (-1)) = 7 |
6,914 | a^2 + a \times 4 + 21 \times (-1) = 0\Longrightarrow 0 = \left(7 + a\right) \times (3 \times (-1) + a) |
-492 | (e^{\frac14\cdot i\cdot 7\cdot \pi})^6 = e^{6\cdot 7\cdot \pi\cdot i/4} |
18,233 | \sin(-z + \frac12\times \pi) = \cos{z} |
-30,427 | 6 = 1 \cdot 1 + 3 + x = 4 + x |
-9,127 | x\cdot x\cdot 2\cdot 2\cdot 5 - x\cdot 2\cdot 2\cdot 5 = x \cdot x\cdot 20 - x\cdot 20 |
2,119 | \cos{2014 \cdot \pi/12} = \cos(\frac{\pi}{12} \cdot 2014 - 2 \cdot \pi \cdot 83) |
6,746 | \cos(2*x) = (-1) + \cos^2\left(x\right)*2 |
-11,483 | i*30 + 20 = -5 + 25 + 30*i |
37,417 | -x^2*2 + 8 = -\left(2 + x\right) (x + 2(-1))*2 |
14,894 | x\cdot 2 + x^2 = x + x\cdot (x + 1) |
6,230 | \left(2/3\right)^3 = q^3*p^3 \implies q * q * q = \frac{8}{p^3*27} |
-15,832 | 30/10 = 6*\frac{8}{10} - 2/10*9 |
24,491 | 1 - 1/2 = \dfrac{1}{1 \cdot 2} |
-25,061 | 6/12\cdot \dfrac{5}{11} = \frac{1}{132}\cdot 30 = 5/22 |
-24,549 | \frac{35}{4 + 1} = 35/5 = \frac15 \cdot 35 = 7 |
2,926 | \left(x + 3 \cdot (-1)\right) \cdot (2 + x) = x^2 - x + 6 \cdot (-1) |
-5,269 | 10^{0 + 4}*31.5 = 10^4*31.5 |
-12,022 | 7/24 = \frac{1}{4\pi}s*4\pi = s |
34,103 | 5\times 10 + 5 = 5 + 50 |
21,612 | X^{n_1} \cdot C^{n_2} = C^{n_2} \cdot X^{n_1} |
-3,868 | \frac{a^4*48}{96*a^2}*1 = \frac{1}{a * a}*a^4*48/96 |
40,631 | 1 = \sin(\frac{1}{2}\pi) |
1,455 | (\pi\cdot (-2))/2 = -\pi |
-13,834 | \frac{1}{5 + 9} \cdot 42 = 42/14 = \frac{1}{14} \cdot 42 = 3 |
52,481 | 11 \times 11 = 121 |
-7,147 | \frac{1}{12}\cdot 3\cdot \frac{3}{11} = \tfrac{3}{44} |
1,748 | a^2\cdot b^2\cdot c \cdot c = (a^2\cdot c + a\cdot b^2)\cdot (a\cdot c^2 + b^2\cdot c) = a^3\cdot c^3 + 2\cdot a^2\cdot b^2\cdot c \cdot c + a\cdot b^4\cdot c |
30,726 | x^2\cdot 2 + x\cdot 3 + 1 = (1 + x)\cdot (2\cdot x + 1) |
-16,819 | -6 = -6 \cdot (-5 \cdot z) - -6 = 30 \cdot z + 6 = 30 \cdot z + 6 |
-2,654 | \sqrt{45} + \sqrt{80} = \sqrt{9 \cdot 5} + \sqrt{16 \cdot 5} |
-10,444 | -20 = 15 \times p + 3 \times (-1) + 18 = 15 \times p + 15 |
18,755 | D \cdot d = D \cdot d |
31,417 | \dfrac{(2 + 1)!}{1!\cdot 2!} = 3 |
37,970 | (\left(-1\right) + (1 + l)*2)*\frac{\pi}{3} = \left(l*2 + 1\right)*\pi/3 |
2,527 | det\left(\frac{1}{Y^2}\right) = -1/64 = det\left(\frac{1}{Y}\right)*(-4) |
15,347 | x^4 = x^2 + 4 \cdot x + 4 = -2 \cdot x + 2 = -2 \cdot (x + (-1)) |
43,260 | \frac{100}{10^4} = 0.01 |
-29,454 | 7/10\cdot (-8/5) = p - -8/5\cdot (-\dfrac{8}{5}) = p |
-16,420 | 12 \cdot 4^{\frac{1}{2}} \cdot 11^{1 / 2} = 12 \cdot 2 \cdot 11^{\frac{1}{2}} = 24 \cdot 11^{\dfrac{1}{2}} |
-29,117 | ({3.3} \times{10^{-4}}) \times ({8.0} \times{10^{0}}) = ({3.3} \times{8.0}) \times ({10^{-4}} \times{10^{0}}) |
-5,341 | 10^1 \cdot 5.7 = 5.7 \cdot 10^{2 + (-1)} |
19,498 | 6 = (-\sqrt{-5} + 1) \times (\sqrt{-5} + 1) |
28,834 | \cos{z} = 2\cos^2{z/2} + (-1) = 1 - 2\sin^2{\frac12z} |
2,467 | \frac{1}{4 \cdot (-1) + 10} = 1/6 |
-11,792 | 125^{-\frac13} = (1/125)^{1/3} = \frac{1}{5} |
5,629 | (-1) + x^1 = (-1) + x |
10,429 | 4\vartheta^2 - 4\vartheta + 3(-1) = \left(1 + 2\vartheta\right) (3(-1) + 2\vartheta) |
23,384 | \frac{1 - \tfrac{1}{x + (-1)}}{x + 2 \cdot (-1)} \cdot (-\frac1x + 1) = \frac{1}{x} |
31,652 | c^2 * c = d^2\Longrightarrow (d/c) * (d/c) = c |
2,219 | x_w \cdot G_w = x_w \cdot G_w |
-8,046 | \frac{1}{4\cdot i - 1}\cdot (i + 4) = \frac{-4\cdot i - 1}{-1 - 4\cdot i}\cdot \frac{4 + i}{-1 + 4\cdot i} |
-7,952 | (-65 + 90*i + 26*i + 36)/29 = (-29 + 116*i)/29 = -1 + 4*i |
3,906 | \frac{s\cdot \frac{1}{s^2 + a^2}}{a^2 + s^2} = \frac{1}{(s^2 + a^2)^2}\cdot s |
-3,787 | \frac{x^4}{x} = \frac{x}{x} \cdot x \cdot x \cdot x = x^3 |
20,523 | \pi/4 + \dfrac{\pi}{2}\cdot 3 = \pi\cdot 7/4 |
-5,825 | \dfrac{3*n}{(n + 7)*(6*(-1) + n)}*1 = \frac{n*3}{n^2 + n + 42*\left(-1\right)} |
35,964 | 21 = 0 \times \left(-1\right) + 21 |
15,329 | x + 1 + x = 2\cdot x + 1 |
-5,735 | \frac{4}{(4*(-1) + z)*3} = \frac{4}{3*z + 12*(-1)} |
-7,707 | \frac{1}{25}*(40 - 80*i + 30*i + 60) = (100 - 50*i)/25 = 4 - 2*i |
31,375 | 0 = \frac{4}{a^3} + \dfrac2a - \frac{b}{a^2} = \dfrac{1}{a^3} \cdot (4 + 2 \cdot a^2 - b \cdot a) |
-4,493 | \frac{21 \cdot (-1) + 9 \cdot x}{4 + x \cdot x - x \cdot 5} = \frac{4}{x + \left(-1\right)} + \frac{1}{x + 4 \cdot (-1)} \cdot 5 |
-5,389 | 0.36*10^6 = 0.36*10^{2*(-1) + 8} |
22,406 | \left(U_1 + U_2\right) Xa = U_1 Xa + Xa U_2 |
-25,049 | \dfrac{5}{13} \cdot \dfrac{4}{12} = \dfrac{20}{156} = \dfrac{5}{39} |
-10,653 | \frac{135}{45 + p \cdot 15} = \frac{1}{3 + p} \cdot 9 \cdot \dfrac{1}{15} \cdot 15 |
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