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19,824 | -\frac{1}{1 + a} + \frac{1}{-a + 1} = \frac{a\cdot 2}{-a \cdot a + 1}\cdot 1 |
-1,767 | \pi \cdot 5/6 = \pi \cdot \frac{19}{12} - \frac{3}{4} \cdot \pi |
22,149 | \left(z_2 = z_1 + 1/(z_1) \Rightarrow 0 = 1 + z_1^2 - z_2\cdot z_1\right) \Rightarrow (z_2 ± \left(z_2^2 + 4\cdot (-1)\right)^{1/2})/2 = z_1 |
14,796 | e^y = \sum_{n=0}^\infty y^n/n! \gt \frac{y^n}{n!} |
24,956 | -a^{2\cdot x} = -a^{2\cdot x} = -a^{2\cdot x} |
25,629 | \mathbb{E}[X+Y]=\mathbb{E}[X]+\mathbb{E}[Y] |
22,725 | (2 \cdot k + 1)^2 = 4 \cdot k \cdot k + 4 \cdot k + 1 = 4 \cdot \left(k^2 + k\right) + 1 |
-16,750 | 3 = 3 \cdot 3 \cdot k + 3 \cdot (-7) = 9 \cdot k - 21 = 9 \cdot k + 21 \cdot (-1) |
-20,943 | \frac{1}{q*40}*(q*30 + 40) = 5/5*\frac{1}{q*8}*(6*q + 8) |
19,671 | \sum_{k=1}^x \left((1 + k)! - k!\right) = \sum_{k=1}^x (1 + k)! - \sum_{k=1}^x k! |
-6,296 | \frac{1}{(x + 6) \cdot 4} = \dfrac{1}{x \cdot 4 + 24} |
-1,976 | 3/4 \cdot \pi = -\pi \cdot 2/3 + \dfrac{17}{12} \cdot \pi |
-2,414 | 6^{1/2}\cdot \left(3 + 2\right) = 6^{1/2}\cdot 5 |
-4,622 | (2 \times (-1) + y) \times (y + 1) = 2 \times (-1) + y^2 - y |
7,880 | 5/2 - \frac73 = \dfrac{1}{6} |
-3,034 | \sqrt{9} \cdot \sqrt{6} + \sqrt{16} \cdot \sqrt{6} = \sqrt{6} \cdot 3 + 4 \cdot \sqrt{6} |
5,751 | -\dfrac{2}{s^2 + (-1)} + \frac{1}{(-1) + s} = \tfrac{1}{1 + s} |
-17,206 | \dfrac{1}{\sec^2{\theta}} \cdot \left(1 + \tan^2{\theta}\right) = \dfrac{1}{\sec^2{\theta}} \cdot \sec^2{\theta} |
-7,672 | \frac{19\cdot i + 8}{4 - 3\cdot i}\cdot \frac{3\cdot i + 4}{4 + i\cdot 3} = \frac{1}{4 - 3\cdot i}\cdot (19\cdot i + 8) |
-233 | \frac{7!}{\left(5 \cdot (-1) + 7\right)! \cdot 5!} = \binom{7}{5} |
-7,333 | \frac{2}{10} \cdot \frac39 = 1/15 |
11,175 | x = \frac{1}{y + 4 \cdot (-1)} \cdot \left(y + 3 \cdot (-1)\right)\Longrightarrow y = \dfrac{1}{x + (-1)} \cdot \left(x \cdot 4 + 3 \cdot \left(-1\right)\right) |
7,021 | 2 + x*2 = 1 + (1 + x)^2 - x^2 |
-501 | -16\cdot \pi + \dfrac13\cdot 52\cdot \pi = \pi\cdot \frac43 |
-20,747 | \tfrac{1}{x \cdot (-4)} \cdot \left(x \cdot (-18)\right) = \dfrac{x \cdot (-2)}{\left(-2\right) \cdot x} \cdot \frac{9}{2} |
3,613 | b + 1 = 1 + b |
28,550 | \dfrac{1}{\cos{y}}\sin{y} = \tan{y} |
9,221 | -6\cdot x - 24 = -(12 + 3\cdot x)\cdot 2 |
4,380 | \left(S + T\right)*(x_1 + x_2) = \left(S + T\right)*x_2 + (T + S)*x_1 |
-3,397 | -13^{1/2} + 117^{1/2} = (9*13)^{1/2} - 13^{1/2} |
22,509 | \sin\left(8x\right) = \sin(5x + 3x) = \sin(5x) \cos(3x) + \sin\left(3x\right) \cos(5x) |
-2,001 | \pi \cdot \dfrac{11}{12} - \pi \cdot 2/3 = \pi/4 |
33,315 | 13+16+19=48 |
-3,924 | \frac{1}{r^5}r^4 \cdot \frac{1}{22}6 = \frac{6r^4}{22 r^5} |
8,292 | \cos{y} = (e^{i y} + e^{-i y})/2 \sin{y} = \frac{1}{2 i} (e^{i y} - e^{-i y}) |
17,998 | (n + (-1))*\left(n + \left(-1\right)\right)! + \left(n + 2*(-1)\right)*(n + (-1))! = \left(n + (-1)\right)!*(n + (-1) + n + 2*(-1)) = (n + (-1))!*(2*n + 3*(-1)) |
15,911 | \left(f + x\right)^2 = f \cdot f + x\cdot f\cdot 2 + x^2 |
11,572 | exp(n + 1) = exp(n) \cdot e^1 = e^n \cdot e^1 = e^{n + 1} |
18,538 | \frac{1}{80}\cdot 40 = \frac{1}{2} |
12,992 | (E + C)^2 = C^2 + E^2 + C \times E + E \times C |
12,269 | \mu_x = k_x\cdot d + \left(k_x + 1\right)\cdot f rightarrow k_x = \dfrac{1}{d + f}\cdot (-f + \mu_x) |
31,411 | 2^m + \left(-1\right) - |y| + 1 = 2^m - |y| = 2^m + y |
7,818 | h\cdot (d + x) = h\cdot x + d\cdot h |
47,370 | 600 = 2 \cdot \left(100 + 100 + 100\right) |
12,299 | 11\cdot \left(-1\right) + 12^2 = 133 |
13,916 | \left(z_1 \cdot z_2\right)^2 = z_1 \cdot z_2 \cdot z_1 \cdot z_2 = z_1^2 \cdot z_2 \cdot z_2 = z_1 \cdot z_2 |
34,443 | b^2 - d * d*4 = (b - 2d) (d*2 + b) |
19,449 | 41 = \left(-2 + \sqrt{5}\cdot 3\right)\cdot (2 + \sqrt{5}\cdot 3) |
27,293 | m^2 + 1 = m \cdot m + 1^2 |
2,040 | \cos(y) = -\sin^2(y/2)*2 + 1 |
3 | 100 ea + (xa + be)*10 + bx = (10 e + x) (b + 10 a) |
15,923 | (10 - b)^2 = 100 - 20 b + b^2 |
28,363 | \frac16 \times ((-1) + 5) = 2/3 |
26,393 | \dfrac{1}{1 - r}\cdot (-r^3 + 1) = 1 + r \cdot r + r |
53,000 | \chi = \chi |
22,256 | \dfrac{1}{\sqrt{2}} = 1/(2 \sqrt{2}) + 1/(2 \sqrt{2}) |
28,292 | \left(a + b\right)^2 = 100 = a \cdot a + 2\cdot a\cdot b + b^2 rightarrow -\frac{1}{2}\cdot (b \cdot b + a^2) = b\cdot a |
3,411 | -\dfrac{1}{16}\cdot \pi + \frac{3\cdot \pi}{16} = \frac{1}{8}\cdot \pi |
-9,336 | 36q^3 - 36q^2 = (2\cdot2\cdot3\cdot3 \cdot q \cdot q \cdot q) - (2\cdot2\cdot3\cdot3 \cdot q \cdot q) |
-4,526 | -\frac{2}{2 + x} - \frac{4}{x + (-1)} = \frac{-6x + 6(-1)}{x^2 + x + 2(-1)} |
-1,203 | \frac{1}{8*\frac{1}{3}}*(\frac{1}{7}*(-9)) = -\frac97*\frac38 |
-578 | e^{14 \cdot \dfrac{\pi}{3} \cdot i} = (e^{i \cdot \pi/3})^{14} |
1,367 | ((\dfrac12)^2)^4 = 1/256 |
19,007 | \dfrac{1}{2} = \tfrac{1}{4} + 1/4 |
5,647 | z^4 - z^2\cdot 4 + 2 = \left(z^2 + 2\cdot (-1)\right) \cdot \left(z^2 + 2\cdot (-1)\right) + 2\cdot \left(-1\right) |
33,725 | \frac12*(-1 + \sqrt{-3}) = -\frac12 + \sqrt{3}*\mathrm{i}/2 |
17,374 | (1 - x^2/3 + x^4/5 - \frac{x^6}{7} + \dotsm)^{-1} = x/\arctan{x} |
31,027 | l = 2 + 3\cdot m rightarrow l\cdot l/3 = 1 + 3\cdot m^2 + 4\cdot m |
-25,001 | 0 + \dfrac{8}{10} + \dfrac{3}{100} + \dfrac{4}{1000} + \dfrac{2}{10000} = \dfrac{8342}{10000} |
38,429 | \binom{9 + 3 + \left(-1\right)}{(-1) + 3} = 55 |
-8,046 | \frac{4 + i}{-1 + i\cdot 4} = \frac{1}{-1 + i\cdot 4}(4 + i) \frac{1}{-1 - 4i}\left(-i\cdot 4 - 1\right) |
7,954 | c = m \cdot r rightarrow r = \frac{1}{m} \cdot c |
17,746 | \tfrac{1}{b*f} = \frac{1}{b*f} |
-23,211 | \frac32\cdot (-\frac{21}{2}) = -63/4 |
51,402 | \begin{pmatrix}10 + 1 & 0 & -3 & 2 & 4\\5 & 35 + 6 & 7 & 8 & -9\\1 & 1 & 5 + 1 & 1 & 1\\0 & 0 & 0 & 1 + 1 & 0\\2 & -3 & 2 & -3 & 14 + 4\end{pmatrix} = \begin{pmatrix}11 & 0 & -3 & 2 & 4\\5 & 41 & 7 & 8 & -9\\1 & 1 & 6 & 1 & 1\\0 & 0 & 0 & 2 & 0\\2 & -3 & 2 & -3 & 18\end{pmatrix} |
-7,375 | \frac{1/9}{8}\times 2 = \frac{1}{36} |
15,322 | b^3 + a^3 + 3 \cdot a^2 \cdot b + 3 \cdot a \cdot b^2 = (a + b) \cdot (a + b) \cdot (a + b) |
3,046 | k*4 = -(2*(-1) + k) - 2 + 2*k + k*3 |
-11,580 | -8 - i\cdot 6 = -9 + 1 - 6\cdot i |
-3,362 | 2\sqrt{13} + \sqrt{13} = \sqrt{13} + \sqrt{4} \sqrt{13} |
12,858 | \|h + b*i\|^{2*x} = (h^2 + b^2)^x = \|(h + b*i)^x\|^2 |
28,196 | \cos(u) \sin\left(u\right)\cdot 2 = \sin\left(u\cdot 2\right) |
3,624 | v \cdot G_0 \cdot v = v \cdot G_0^{1/2} \cdot G_0^{\frac{1}{2}} \cdot v = G_0^{1/2} \cdot v |
940 | 3 \cdot (-1) + 3 \cdot n = n + 2 \cdot (-1) + n + n + (-1) |
-17,559 | 28 \cdot (-1) + 35 = 7 |
19,450 | 269/8 + (x\cdot 2 + 5\cdot \left(-1\right))\cdot (49 + 4\cdot x^2 + 10\cdot x)/8 = x^3 + 6\cdot x + 3 |
-9,780 | 24\% = \frac{1}{100}\times 24 = 0.24 |
8,115 | \frac{y}{\sqrt{1 + y \cdot y}} = \sin(\tan^{-1}(y)) |
6,166 | 36/7 \cdot \left(1/4 + 7 \cdot y/12\right) - \frac{9}{7} = y \cdot 3 |
9,944 | 1 + \dfrac{2}{3} = \frac{1}{3}\cdot 5 |
11,619 | 3^{4\cdot k} = 9^{2\cdot k} |
21,722 | \frac{1}{10} + 1/15 = 3/30 + 2/30 = \frac{5}{30} |
45,715 | 38 = 2\cdot 19 |
16,285 | \dfrac{1}{(k + \left(-1\right))!} \cdot k! = k |
32,208 | x^2 - 4*x + 120 = x^2 - 4*x + 4 + 116 = \left(x + 2*(-1)\right)^2 + 116 |
1,351 | BA*(-x + A) = AB*\left(-x + A\right) |
13,835 | a_2 a_1 a_3 = a_2 a_3 a_1 |
20,635 | \left(n + k\right) \cdot (l + i) = n \cdot l + k \cdot l + i \cdot n + i \cdot k |
29,997 | 3^{4 + 7 \cdot (-1)} = 1/27 = \dfrac{1}{3^3} |
-3,995 | 7l/6 = l\frac{7}{6} |
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