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9,544 | x_{l + \left(-1\right)} + x_{2 (-1) + l} = x_l \Rightarrow -x_{2 \left(-1\right) + l} + x_l = x_{(-1) + l} |
-20,929 | 81/(-18) = -9/(-9) \left(-\frac{9}{2}\right) |
15,935 | \frac{2^0 + (-1)}{2 + 0} = 0 |
14,446 | 3/11 = \frac{1\cdot 3}{4\cdot 2 + 1\cdot 3} |
-9,380 | -2 \times k + 16 = -k \times 2 + 2 \times 2 \times 2 \times 2 |
41,797 | \frac{1}{100}\cdot 95\cdot 60 = 57 |
5,674 | Q = Q^\complement = Q |
5,326 | \frac{\partial}{\partial x} (w_1 \cdot w_2) = \frac{\partial}{\partial x} w_2 \cdot w_1 + \frac{\partial}{\partial x} w_1 \cdot w_2 |
29,900 | 4^2 + 10^2 + 28^2 = 15^2 \cdot 4 |
-19,734 | \frac58 \cdot 7 = 35/8 |
-4,415 | (y + 4) \cdot (y + 1) = 4 + y^2 + 5 \cdot y |
19,058 | 3/2 - x = x \cdot 2 - 6 \Rightarrow \frac52 = x |
11,626 | |4^2 - 14\cdot 1^2| = 2 |
16,660 | -101 = (-13) \cdot 7 + 10 \cdot \left(-1\right) = (-8) \cdot 13 + 3 |
24,197 | \frac{5x+6}{(2+x)(1-x)} = \frac{\frac52 x + 3}{\left(1+\frac12 x\right)(1-x)} |
36,761 | \dfrac{8}{27} = 1/405\cdot 120 |
-16,375 | \sqrt{4*2}*12 = 12 \sqrt{8} |
10,088 | \left(d^2 + d \cdot b + b^2\right) \cdot \left(-b + d\right) = d^2 \cdot d - b^3 |
27,422 | z = \left(z^{1/2}\right)^2 |
-10,655 | \frac{t \cdot 6 + 30}{t \cdot 12} = \frac{1}{t \cdot 2} (t + 5) \cdot 6/6 |
-28,770 | \tfrac{1}{2\cdot x + 6} + \frac12 = \frac{x + 4}{6 + 2\cdot x} |
26,559 | (z + 2)\times \left(3\times z + 8\right) = 16 + 3\times z \times z + 14\times z |
25,848 | E(E(Q) \cdot Y) = E(Q) \cdot E(Y) |
38,015 | 1 + 2 + 1 = 1 + 1 + 2 |
35,529 | \frac{y^a}{y^c} = y^{a - c} = \frac{1}{y^{c - a}} |
8,324 | -2 \cdot (k + 1) + 3 \cdot k + 2 = k |
8,873 | \binom{k + i}{i} = -\binom{i + k}{i + (-1)} + \binom{i + k + 1}{i} |
-11,715 | (\frac{8}{5}) \cdot (\frac{8}{5}) = \frac{64}{25} |
-28,816 | \frac12 \cdot \left(2 + 6\right) = \dfrac{1}{2} \cdot 8 = 4 |
1,854 | |\lambda|\cdot B\cdot |\mu|\cdot C = C\cdot B\cdot |\mu|\cdot |\lambda| |
-14,616 | 90 = \dfrac{1}{9}810 |
27,242 | \left(2*a + 2*b + c\right)/3 = \dfrac15*(3*a + 4*c) = \frac{1}{3}*(2*a + b + 2*c) |
15,824 | 0 \leq y + \sqrt{26} \Rightarrow -\sqrt{26} \leq y |
-18,592 | -\frac{16}{11} = - \frac{16}{11} |
23,530 | c_2^2 - c_1^2 = (c_1 + c_2)*(c_2 - c_1) |
21,944 | (2^{33} + (-1))*(2^{33} + 1) = 2^{66} + \left(-1\right) |
-7,147 | 3/11*\frac{3}{12} = 3/44 |
-1,281 | -35/14 = \frac{(-35)\cdot 1/7}{14\cdot \frac17} = -5/2 |
23,789 | (AA^Z)^Z = (A^Z)^Z A^Z = AA^Z |
28,904 | \frac{1}{2}\cdot (i + l + 2\cdot (-1))\cdot (i + l + \left(-1\right)) = \sum_{m=1}^{i + l + 2\cdot \left(-1\right)} m = \sum_{m=2}^{i + l + (-1)} (m + (-1)) |
25,715 | (-1) + x^6 = ((-1) + x) \cdot (1 + x^2 + x) \cdot (x^3 + 1) |
-30,096 | d/dy \left(5 + 2\cdot y^2 - 6\cdot y\right) = 4\cdot y + 6\cdot \left(-1\right) |
22,760 | \operatorname{Var}\left(1.08 \cdot R + B\right) = \operatorname{Var}\left(B + 500 + R \cdot 1.08\right) |
10,798 | 2 \cdot l + 6 \cdot (-1) = 0 \Rightarrow l = 3 |
-27,514 | 6a = 2*3a |
20,806 | a + b = ( a, b) ( 1, 1) \leq (a^2 + b^2)^{\frac12} |
25,220 | \left(T_1 + T_2\right)^2 - T_2 \times T_1 \times 2 = T_1 \times T_1 + T_2^2 |
30,112 | \cos{\frac{4*\pi}{9}}*2 = 2*\sin{\pi/18} |
-23,062 | \frac{1}{27} \cdot 16 \cdot \left(-\dfrac{2}{3}\right) = -\frac{32}{81} |
37,408 | \left( w_1, w_2\right) + ( 0, 0) = ( w_1 + 0, w_2 + 0) = [w_1, w_2] = ( 0, 0) + \left( w_2, w_1\right) |
13,841 | \cosh(p) = \left(e^p + e^{-p}\right)/2 = \cos(i\cdot p) |
633 | \left(x^n + a^n \Leftrightarrow x + a = 0\right) \implies 0 = a^n + x^n |
23,303 | y\cdot x^3 = b + \int x \cdot x \cdot x\cdot x\,\mathrm{d}x \Rightarrow x^5/5 + b = y\cdot x^3 |
21,132 | r + y * y*s + t*y = \pi*(4*k + 1) \Rightarrow 0 = s*y^2 + y*t + r - \left(k*4 + 1\right)*\pi |
1,385 | \frac16\times \frac26 = \frac2{36} |
-24,447 | \frac{1}{8 + 9}*170 = \frac{170}{17} = \frac{170}{17} = 10 |
30,531 | \left( u, v\right) + ( 0, 1) = ( u + 0, v) = [u, v] |
15,895 | qF = bF \Rightarrow F/b = F/q |
14,936 | (\mathbb{E}[Q]^2 + \mathbb{Var}[Q])/2 = \mathbb{E}[Q^2/2] |
6,213 | f = z\cdot Y \Rightarrow z = f/Y |
4,690 | 426*5!^3/15! = \frac{1}{126126}71 \approx 0.00056292 |
16,664 | 8 = a + h\Longrightarrow -h + a = 2 |
22,650 | (x + f)^2 = f^2 + x \cdot x + 2\cdot x\cdot f |
21,546 | \frac{1}{m \cdot k + 2 \cdot (-1)} \cdot (-((-1) + m) \cdot 2 + m \cdot k + 2 \cdot (-1)) = \dfrac{m}{k \cdot m + 2 \cdot (-1)} \cdot (2 \cdot (-1) + k) |
26,596 | z^2 - 3 \cdot z + 2 = ((-1) + z) \cdot (2 \cdot (-1) + z) |
20,493 | \sin(3\cdot A) = \sin(3\cdot (4\cdot \pi/3 + A)) |
10,383 | \int\limits_a^b k\,\text{d}y = \int_a^b k\,\text{d}y |
-22,619 | -7/8\cdot \frac{1}{4}3 = \frac{1}{8\cdot 4}((-7)\cdot 3) = -\frac{21}{32} = -\dfrac{21}{32} |
19,775 | \frac{1}{n^2} \cdot n \cdot i = i/n |
20,846 | \mathbb{E}\left[Q\right] = \mathbb{E}\left[\sum_{j=1}^k Q_j\right] = \sum_{j=1}^k \mathbb{E}\left[Q_j\right] |
-22,097 | \frac{1}{12} \cdot 20 = \frac{5}{3} |
23,147 | -4*i = 4*(\cos{-\frac{\pi}{2}} + i*\sin{-\frac{\pi}{2}}) = -4*i |
-22,243 | q^2 + 10 \cdot q + 21 = (q + 3) \cdot (q + 7) |
-22,868 | 110/66 = \frac{22 \cdot 5}{22 \cdot 3} |
-25,584 | \frac{3}{x^2} = d/dx (-\dfrac3x) |
-3,143 | 13^{\dfrac{1}{2}}\cdot (4 + 1) = 5\cdot 13^{1 / 2} |
11,386 | y^4 - y^3 + y^3 + (-1) = y^4 + \left(-1\right) |
28,137 | m_l \times m_i = m_i \times m_l |
17,238 | (f + g*i)^{-1} = (g*i + f)^{-1} |
17,990 | 2*\sqrt{3} + 4 = (1 + \sqrt{3})*(1 + \sqrt{3}) |
12,557 | \frac{1}{\left(m + 1\right)!}\cdot m! = \dfrac{m!}{(m + 1)\cdot m!} = \frac{1}{m + 1} |
11,449 | -\sin(\frac56 \cdot \pi) \cdot (-1) - \sin(\pi/6) = 0 |
15,176 | z_x = f' x \cdot 2 y \Rightarrow xf' y \cdot y^2 \cdot 2 = y^2 z_x |
30,875 | x^4 + 4 \cdot y^4 = (x^2 + 2 \cdot y^2) \cdot (x^2 + 2 \cdot y^2) - (2 \cdot x \cdot y)^2 = (x^2 + 2 \cdot x \cdot y + 2 \cdot y^2) \cdot (x^2 - 2 \cdot x \cdot y + 2 \cdot y^2) |
-28,922 | \dfrac{7}{7 \times \frac{1}{20}} = 7 \times \dfrac{20}{7} = 20 |
33,233 | \frac12 \cdot 3200 + \frac{800}{2} = 2000 |
-12,907 | 8/18 = \frac19 \cdot 4 |
23,124 | \frac{x}{4}*x * x + \frac{x*x^2}{4} + A = A + \frac{x^3}{2} |
18,463 | -y^k + \left(1 + k\right)^2\cdot y^k - k\cdot y^k\cdot 2 = k^2\cdot y^k |
37,910 | \frac{i +1}{1 +i} =1 |
14,743 | -(1 + i) (i + 1 + 2(-1)) + z \cdot (i + 1 + (-1)) = -\left(i + 1\right) (i + (-1)) + zi |
27,551 | z_1 \cdot r_1 + \dotsm + z_k \cdot r_n = \overline{r_1} \cdot z_1 + \dotsm + z_k \cdot \overline{r_n} |
6,595 | (g + (-1)) \cdot \left(1 + g^2 + g\right) = g^3 + (-1) |
23,612 | \cos\left(-y + z\right) = \sin{y}\cdot \sin{z} + \cos{y}\cdot \cos{z} |
-10,535 | \tfrac{4}{4}\cdot \dfrac{1}{m + 3\left(-1\right)}10 = \dfrac{40}{12 (-1) + m\cdot 4} |
2,894 | 4\cdot (18\cdot t - 6\cdot i + 10) + 6\cdot i + 4\cdot (-1) = 72\cdot t - 24\cdot i + 40 + 6\cdot i + 4\cdot (-1) = 18\cdot (4\cdot t - i + 2) |
532 | \frac{\mathrm{d}}{\mathrm{d}x} \sin^{-1}(x) = \frac{1}{\cos\left(\cos^{-1}\left(x - \pi/2\right)\right)} |
28,364 | -\frac{1}{(1 - x)^2} = -\frac{1}{\left(1 - x\right) \cdot \left(1 - x\right)} |
21,627 | x^2 + x + 1 = (1 + x^2 + x) + 0 |
-20,616 | 30/(-18) = -6/\left(-6\right)\cdot (-\frac{5}{3}) |
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