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26,116 | 2 \times \cos(\tfrac12 \times H) \times \sin(H/2) = \sin(H) |
20,220 | -y^2 + z^2 = \left(z - y\right)*(y + z) |
35,079 | \sqrt{a - b \cdot \sqrt{a + b \cdot \sqrt{a - b \cdot \sqrt{a + \dots}}}} = \sqrt{-b^2 \cdot 3/4 + a} - \dfrac{b}{2} |
26,393 | \frac{1}{-s + 1} \cdot \left(1 - s^3\right) = 1 + s^2 + s |
2,316 | 0 = 2zy' + 4x \Rightarrow -\dfrac{2x}{z} = y' |
13,995 | \frac{1}{27} \cdot M = \frac{M}{3^3} |
28,211 | \sin{(3/2 + x)\cdot 2} = \sin(3 + x\cdot 2) |
15,271 | 1 + 4 \cdot e + e^2 \cdot 9 + \ldots + e^{\left(-1\right) + n} \cdot n \cdot n = e \cdot n \cdot n - n \cdot e^2 \cdot 2 |
-7,706 | \frac{-5 - i \cdot 25}{-i + 5} = \tfrac{5 + i}{5 + i} \cdot \frac{1}{-i + 5} \cdot (-5 - i \cdot 25) |
21,022 | F\cdot z = b \Rightarrow \frac{b}{F} = z |
3,820 | (h + g + d) \cdot (-d \cdot h + g^2 + d^2 + h \cdot h - h \cdot g - d \cdot g) = -3 \cdot g \cdot d \cdot h + g^3 + d^3 + h^3 |
31,822 | -(l^2 + (-1)) + 2*l^2 = l * l + 1 |
-11,570 | -18 i + 15 + 3(-1) = 12 - i\cdot 18 |
12,722 | g^2 + H = g + g + H = \left(g + H\right)*(g + H) = (g + H)^2 |
12,707 | \dfrac{0.765}{0.85} = 0.9 |
-679 | e^{12\cdot \frac{i\cdot \pi}{12}\cdot 1} = (e^{\frac{\pi}{12}\cdot i})^{12} |
-20,215 | \frac{35\cdot x + 30}{24\cdot (-1) - 28\cdot x} = -5/4\cdot \frac{1}{-7\cdot x + 6\cdot \left(-1\right)}\cdot (-x\cdot 7 + 6\cdot \left(-1\right)) |
-4,507 | -\frac{1}{x + 2(-1)}5 + \frac{2}{x + 5\left(-1\right)} = \dfrac{1}{x^2 - 7x + 10}\left(21 - x\cdot 3\right) |
24,023 | 4\times x\times y\times z_1\times ...\times ...\times ...\times ...\times ...\times ...\times ...\times ...\times 2 = x^2 + y^2 + z_1^2\times 4 |
-10,559 | 24/(y*75) = 3/3*8/(y*25) |
15,427 | \left(a + y\right) (-a + y) = -a^2 + y^2 |
-1,680 | \pi*5/3 = \pi*\frac12*3 + \pi/6 |
-1,682 | \pi/2 + \frac14*3*\pi = \frac54*\pi |
25,189 | 4*x = 4*x = x + x + 1/4 + x + \frac24 + x + \frac{3}{4} |
-19,473 | 1/(3*\tfrac187) = 8*1/7/3 |
16,941 | -\dfrac{7*6}{7} + 6 = 0 |
6,036 | x + z + 2\cdot y = x + y + y + z |
-6,731 | 8/100 + 10/100 = 10^{-1} + \frac{1}{100}*8 |
-1,675 | 2*\pi - 3/4*\pi = \pi*\frac{1}{4}*5 |
-19,460 | \frac{7 \cdot \frac{1}{5}}{8 \cdot 1/9} = 9/8 \cdot 7/5 |
-4,335 | \frac{x\cdot 60}{50\cdot x^3} = \tfrac{1}{50}\cdot 60\cdot \frac{x}{x^3} |
2,403 | d \cdot d + 4 + d \cdot 4 = (2 + d) \cdot (2 + d) |
-25,423 | \frac{1}{\cos^2{x}}\cdot (\sin{x}\cdot x + \cos{x}) = \frac{\text{d}}{\text{d}x} (\frac{1}{\cos{x}}\cdot x) |
261 | X^2 = B rightarrow X = B^{1/2} |
16,367 | 5 = 2*(1 + 3/2) |
9,075 | 2*\cos(\dfrac{2*\pi}{5}) + \cos(\frac{4}{5}*\pi)*2 + 1 = 0 |
1,443 | (c + d)/d = c/d + 1 |
-6,561 | \frac{2}{2 \cdot (z + 2 \cdot (-1))} = \tfrac{1}{2 \cdot z + 4 \cdot (-1)} \cdot 2 |
-5,002 | 10^{-1 + 3} \cdot 15.8 = 10 \cdot 10 \cdot 15.8 |
22,018 | (-b + g)\times (b + g) = -b^2 + g^2 |
10,806 | \left((-1) + 2^4\right) \cdot (4 \cdot (-1) + 2^4) \cdot (2^4 - 2^3) \cdot (2 \cdot \left(-1\right) + 2^4) = 20160 |
13,773 | 4/27 = \tfrac{8*1/18}{3} |
-1,175 | -45/12 = ((-45)\cdot \frac13)/(12\cdot \frac13) = -\frac{1}{4}\cdot 15 |
-18,288 | \dfrac{1}{x \cdot (x + 4 \cdot (-1))} \cdot (4 \cdot \left(-1\right) + x) \cdot (4 + x) = \frac{1}{-4 \cdot x + x^2} \cdot (16 \cdot \left(-1\right) + x^2) |
23,445 | (x + 1)\cdot (x + 1) = x^2 + 2\cdot x + 1 = x^2 + 1 = x^1 + 1 - x^2 + x + 1 = -x = -x = x |
21,590 | a + f = \left(a + f\right)^2 = a^2 + af + fa + f^2 = a + af + fa + f |
-5,133 | \frac{1}{1000}66.6 = \frac{66.6}{1000} |
23,476 | e^{\frac143\pi i} e^{\pi i/4} = e^{\pi i} = -1 |
-26,549 | 75 + 3 \cdot y^2 + 30 \cdot y = (y^2 + y \cdot 10 + 25) \cdot 3 |
-1,297 | \frac{1}{\frac{1}{7} \cdot 5 \cdot 4} = 7 \cdot 1/5/4 |
16,376 | y^2 = (y + 2) * (y + 2) - \left(y + 7(-1)\right)^2 = \left(y + 2 + y + 7(-1)\right) (y + 2 - y + 7) = 9*(2y + 5\left(-1\right)) = 18 y + 45 \left(-1\right) |
13,180 | \frac{a}{x} = \sqrt{1 + 4*n}\Longrightarrow n*4 + 2 = \frac{a^2}{x^2} |
-20,265 | \frac{-x*18 + 2(-1)}{-10 x + 18 (-1)} = \frac{\left(-1\right) - 9x}{-5x + 9(-1)} \frac122 |
-6,721 | 8/100 + 40/100 = \frac{4}{10} + \dfrac{1}{100} \cdot 8 |
28,968 | (x^3 + (-1)) * (x^3 + (-1)) = ((x + (-1))*(x^2 + x + 1))^2 = (x + \left(-1\right))^2*(x * x + x + 1)^2 |
25,555 | (z_1 + z_2\cdot 2)^2 + 5 z_2^2 = z_1^2 + 4 z_1 z_2 + z_2^2\cdot 9 |
25,423 | e^{-h} = e^{h\cdot i^2} = \cos(h\cdot i) + i\cdot \sin\left(h\cdot i\right) |
20,630 | (2049 + 320*\sqrt{41})^2 = 1311360*\sqrt{41} + 8396801 |
36,687 | \frac44 + \tfrac14*4 = 1 + 1 = 2 |
33,150 | \sin(Z)*\cos\left(A\right) + \cos(Z)*\sin(A) = \sin\left(Z + A\right) |
13,493 | \operatorname{E}\left[Y\times T\right] = \operatorname{E}\left[Y\right]\times \operatorname{E}\left[T\right] |
-7,423 | \tfrac{1}{3*3} = 1/9 |
9,886 | 10*x - x = 9*x = 9 \implies x = 1 |
-10,447 | \frac{3}{x + 3 \times (-1)} \times \tfrac{6}{6} = \frac{18}{x \times 6 + 18 \times (-1)} |
6,060 | 3 + l^3 + 3l^2 + 5l = l^3 + l\cdot 2 + l^2\cdot 3 + l\cdot 3 + 3 |
7,425 | a\cdot x\cdot y + b\cdot y\cdot z = (a\cdot x + b\cdot z)\cdot y \leq \sqrt{a^2 + b^2}\cdot \sqrt{x^2 + z^2}\cdot |y| |
-1,387 | -1/9*7/9 = \dfrac{(-1)*\frac19}{\frac{1}{7}*9} |
12,326 | \frac{BA^{-\frac12}}{A^{\dfrac{1}{2}}} = \frac{B^{1/2}}{A^{1/2}} \frac{B^{1/2}}{A^{1/2}} |
49,041 | (-1) + 6 + (-1) = 4 |
14,859 | e^{x + w} = e^x*e^w |
11,874 | 1997 + 1997^n*(\left(-1\right) + 1997) = 1997^n*1996 + 1997 |
28,425 | y^g*y = y^{g + 1} |
32,701 | 2 - y_1 \cdot 2 = y_1 |
18,695 | \frac{7}{12} = 1/2 + \frac{1}{4*3} |
13,343 | \frac13 \left(-x \cdot 2 + 3 x\right) = x/3 |
-672 | e^{5\pi i/3} = (e^{\frac{\pi i}{3}})^5 |
-18,739 | 0.849 = (-1)\cdot 0.1151 + 0.9641 |
23,877 | \sin{x} = \sin(x/2 + \frac{x}{2}) = 2\sin{\frac{x}{2}} \cos{\frac{x}{2}} |
-3,204 | \sqrt{2} \sqrt{25} + \sqrt{9} \sqrt{2} = 3\sqrt{2} + 5\sqrt{2} |
2,538 | A_x * A_x + A_z^2 = A * A \implies \sqrt{A_z * A_z + A_x^2} = A |
-4,774 | -\dfrac{1}{y + 2} - \frac{5}{2\left(-1\right) + y} = \dfrac{-6y + 8(-1)}{y^2 + 4(-1)} |
13,419 | 0 < n^2/n! = \frac{n \cdot n}{(n + 2 \cdot (-1))!} \cdot \dfrac{1}{(n + (-1)) \cdot n} \lt \frac{1}{n + 2 \cdot (-1)} \cdot 2 |
-6,589 | \frac{1}{k^2 + 5 \cdot k + 14 \cdot (-1)} = \frac{1}{(k + 7) \cdot (2 \cdot (-1) + k)} |
29,246 | -b \cdot b + g^2 = (g - b) \cdot \left(b + g\right) |
-8,086 | \frac{-1 + i}{-1 + i} \dfrac{i\cdot 7 + 3}{-1 - i} = \frac{i\cdot 7 + 3}{-1 - i} |
20,445 | \frac{y^3 + (-1)}{\left(-1\right) + y} = y^2 + y + 1 |
4,924 | \frac{1}{\varepsilon}\cdot \varepsilon^{1/2} = \frac{\varepsilon^{1/2}}{\varepsilon} = \varepsilon^{-1/2} |
8,264 | \cos(T + \alpha) = \cos(T) \cos\left(\alpha\right) - \sin(T) \sin(\alpha) |
5,519 | \dfrac{8!}{10!} = 1/90 |
-15,859 | -81/10 = \frac{9}{10} - 10\cdot 9/10 |
-7,223 | 10^{-1} = \dfrac{1}{15}\cdot 6\cdot \frac{4}{16} |
-24,722 | (140\cdot a^5)^{1/2} = (2^2\cdot 5\cdot 7\cdot (a \cdot a)^2\cdot a)^{1/2} = \left(2^2\right)^{1/2}\cdot 35^{1/2}\cdot \left((a^2)^2\right)^{1/2}\cdot a^{1/2} = 2\cdot 35^{1/2}\cdot a^2\cdot a^{1/2} = 2\cdot a^2\cdot (35\cdot a)^{1/2} |
10,324 | \frac{1}{9}*5 = -4/9 + 1 |
15,396 | |\overline{A} \cap \overline{B}| = |x \backslash A \cup B| = |x| - |A| - |B| + |A \cap B| |
36,691 | A = \frac{1}{1/A} |
5,718 | \frac{1}{n+1}-\frac{1}{n+2}=\frac{1}{(n+1)(n+2)} |
10,675 | (x - y)*z = -z*y + x*z |
19,728 | a^2 = a^2 + 2\cdot 0 + 0^2 |
25,655 | 4^{100} - 3^{100} = 100*a^{99} = \frac{1}{a}*100*a^{100} |
-4,773 | \dfrac{1}{y \cdot y - y + 2\cdot (-1)}\cdot (2\cdot y + 13\cdot (-1)) = -\frac{3}{y + 2\cdot (-1)} + \frac{5}{y + 1} |
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