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13,265 | a^{-k + l} = \frac{1}{a^k} a^l |
19,612 | |B/E| = \frac{|B|}{|E|} |
13,740 | (2 + k)\cdot \left(k + 2\cdot (-1)\right) = k^2 + 4\cdot (-1) |
15,163 | \dfrac{1}{ha} = 1/(ah) |
-20,829 | \frac{1}{7}*1 = \frac{\left(-1\right) + k}{7*(-1) + 7*k} |
20,255 | 1 \gt 1 - 1/8 = 7/8 = 28/32 \gt \dfrac12 + 1/32 = 17/32 > \dots |
394 | 0*...*\pi*2 = 0 |
23,019 | \frac1x\cdot (a + c) = (-1) + \dfrac1x\cdot (a + x + c) |
7,075 | \frac{3\cdot 17}{4\cdot 17} = \dfrac{51}{68} |
9,975 | 35 \cdot (-1) + 49 \cdot b^2 = 35 \cdot (-1) + 49 \cdot b^2 |
-15,966 | 19/10 = -10\cdot 3/10 + 7\cdot \dfrac{7}{10} |
-22,195 | (x + 2) \cdot (10 + x) = x^2 + x \cdot 12 + 20 |
802 | 1/2 + 1/3 + 1/18 = \frac89 |
21,601 | W^4 = W^2 \cdot W \cdot W |
-3,631 | 70 = 2\cdot 5\cdot 7 |
17,208 | -144 = 9\times (-16) |
8,539 | 1/27 \cdot 4/180 = \frac{1}{1215} |
23,521 | 13 = 4 + 3^2 |
6,119 | \frac{2}{3}\cdot 6\cdot 10 = z\cdot 4/3\Longrightarrow z = 1/3 |
4,086 | (z\cdot y)^2 \cdot (y\cdot z) = z^3\cdot y^3 |
-2,097 | \frac{5}{3} \pi = -\frac{\pi}{3} + \pi\cdot 2 |
30,574 | 26^3 = (6\cdot (-1) + 2^5)^3 |
15,218 | \tan^2(z) = (\sin\left(z\right)/\cos\left(z\right))^2 \approx \frac{1}{(-z + \frac{\pi}{2})^2} |
30,553 | \frac18 \times 120 = 15 |
7,663 | 72\cdot 5 - 48\cdot 7 = 24 |
13,589 | m/2 + \left(-1\right) = \frac{1}{2}\cdot (m + 2\cdot (-1)) |
13,126 | \frac{\sin{z}}{z} = (z - \frac{1}{3!}*z^2 * z + \dfrac{z^5}{5!} - \dots)/z = 1 - z^2/3! + z^4/5! - \dots |
-6,179 | \tfrac{1}{16 + x\cdot 4}\cdot 4 = \frac{4}{(x + 4)\cdot 4} |
1,994 | 4*\left(5*y\right)^2 = 100*y^2 |
-28,771 | -1/2 - \frac{4}{-2 \cdot x + 2} = -\frac12 + \frac{1}{x + \left(-1\right)} \cdot 2 |
32,568 | 1/(\sqrt{l}) = \frac{1}{\sqrt{l} + \sqrt{l}}\cdot 2 \gt \tfrac{1}{\sqrt{l} + \sqrt{l + 1}}\cdot 2 |
25,706 | 2\cdot (x - 1/2) = x\cdot 2 + (-1) |
27,528 | e^{a \cdot z} \cdot a = \frac{\partial}{\partial z} e^{a \cdot z} |
-17,368 | \dfrac{1}{100} 63.3 = 0.633 |
31,134 | \tan{b} = \frac{\sin{b}}{\cos{b}} |
31,594 | |z| < 1 \Rightarrow \dfrac{1}{z + 1} = 1 - z + z^2 - z^3 + \dots |
-20,355 | \dfrac{9}{2}\cdot \frac{1}{x + 2\cdot \left(-1\right)}\cdot (2\cdot (-1) + x) = \tfrac{18\cdot (-1) + x\cdot 9}{x\cdot 2 + 4\cdot (-1)} |
8,912 | -g + x = -g + x |
13,728 | \frac{\text{d}}{\text{d}x} \frac{1}{Z} = \frac1Z \cdot \frac{\text{d}Z}{\text{d}x}/Z |
-4,910 | 3.3 \cdot 10^3 = 10^{8 + 5\left(-1\right)} \cdot 3.3 |
-9,053 | 43.3\% = \frac{43.3}{100} |
-9,318 | -2\cdot 5\cdot 5 - t\cdot 2\cdot 3\cdot 5 = -30\cdot t + 50\cdot (-1) |
11,673 | 24/14.4 = \dfrac53 |
24,707 | \operatorname{atan}(16/63) = \operatorname{atan}(\frac{1}{63}16) |
-10,781 | \frac22\cdot (-\frac{6}{s\cdot 25 + 20\cdot \left(-1\right)}) = -\frac{12}{40\cdot (-1) + 50\cdot s} |
25,263 | \dfrac{1 + \frac{1}{2}}{1 + \frac{1}{4}} = 1.2 \lt 1 + 1/4 |
14,416 | |y^3 + 3\cdot y \cdot y\cdot g + 3\cdot y\cdot g^2 + g^3 - y \cdot y^2| = |3\cdot y^2\cdot g + 3\cdot y\cdot g \cdot g + g^3| \geq 3\cdot y^2\cdot g |
11,979 | \frac{r}{x^2} \cdot d \cdot d = \frac{r \cdot d^2}{x \cdot x} |
11,873 | \infty = x < x + 1 = \infty \Rightarrow x = x + 1 |
5,522 | a\cdot l - l + 1 + 1 = l\cdot (a + (-1)) |
-1,075 | -63/18 = ((-63)\cdot \frac19)/(18\cdot \frac{1}{9}) = -\dfrac{7}{2} |
18,726 | (b^2 + a^2)^{\frac{1}{2}} * (b^2 + a^2)^{\frac{1}{2}} * (b^2 + a^2)^{\frac{1}{2}} = 8 \Rightarrow (a^2 + b^2)^3 = 8 * 8 = (2 * 2 * 2)^2 = 2^6 |
11,559 | 9^2 - 4 \cdot 4\cdot 2 = 49 |
-6,294 | \frac{1}{x^2 - 14*x + 45}*2 = \dfrac{1}{\left(9*(-1) + x\right)*(5*(-1) + x)}*2 |
25,462 | \tfrac{10!}{5!*5!} = 252 |
44,115 | (\sqrt{31 - 8\times \sqrt{15}} + \sqrt{31 + 8\times \sqrt{15}})^2 = 31 - 8\times \sqrt{15} + 31 + 8\times \sqrt{15} + 2\times \sqrt{31^2 - 64.15} = 64 |
26,639 | \frac{\partial}{\partial t} (y\cdot z) = \frac{\text{d}y}{\text{d}t}\cdot z + y\cdot \frac{\text{d}z}{\text{d}t} |
-659 | \left(e^{4 \cdot i \cdot \pi/3}\right)^{10} = e^{10 \cdot \frac{4}{3} \cdot \pi \cdot i} |
-30,239 | (2\cdot (-1) + z)\cdot (10\cdot (-1) + z) = z^2 - z\cdot 12 + 20 |
230 | (C^2 + D^2 - D \cdot C) \cdot \left(D + C\right) = D^3 + C^3 |
5,118 | \left(x + 1\right)! := x! \cdot (1 + x) |
3,427 | |z \cdot E - D \cdot B| = |E \cdot z - D \cdot B| |
26,733 | g_2^{i + 1}\cdot g_1^{i + 1} = (g_2\cdot g_1)^{i + 1} = g_2\cdot g_1\cdot (g_2\cdot g_1)^i = g_2\cdot g_1\cdot g_2^i\cdot g_1^i |
39,490 | 7 \cdot 7^2 = 5 + 13^2 \cdot 2 |
-6,389 | \frac{2}{n\cdot 5 + 45} = \frac{2}{5\cdot \left(9 + n\right)} |
-19,343 | 8*1/7/\left(7*\dfrac{1}{5}\right) = \frac57*\frac17*8 |
575 | (\frac{1}{2})! = \pi^{\frac{1}{2}}/2 |
15,922 | \frac{h^g}{h^c} = h^{-c + g} |
16,766 | (-y)^{1 / 2}\cdot (-y)^{1 / 2} = (-y\cdot (-y))^{1 / 2} = (y^2)^{1 / 2} |
13,332 | 7^2 + 24^2 = 25 \times 25 |
-22,182 | 21/15 = \frac{1}{5} \cdot 7 |
26,038 | \frac18 \cdot \pi \cdot 3 + \pi = \pi \cdot 11/8 |
24,427 | r\cdot m = m\cdot r |
5,203 | \dfrac{6!}{3!\cdot 2!\cdot 1!} = 6\cdot 5\cdot 4/2 = 60 |
-20,940 | \tfrac{54\cdot z + 81\cdot (-1)}{-z\cdot 24 + 36} = \frac{-6\cdot z + 9}{9 - z\cdot 6}\cdot (-\dfrac94) |
-2,103 | \pi/2 - \pi/12 = \pi \cdot 5/12 |
8,683 | z^{t_1} \times z^{t_2} \coloneqq z^{t_1 + t_2} |
8,614 | ((-1) + y^2)\cdot (y^2 + 1) = (-1) + y^4 |
27,670 | \cot(A) - \tan(A) = \left(\cos^2(A) - \sin^2(A)\right)/(\sin\left(A\right) \cos\left(A\right)) = 2\cot(2A) |
27,152 | 1/(2\cdot 2) + \frac{1}{2\cdot 2} = \frac{1}{2} |
8,839 | i^2 + 2*i + 1 = (i + 1)^2 |
11,013 | \left(b + a\right)^3 = a^3 + b a^2 \cdot 3 + a b^2 \cdot 3 + b^3 |
8,389 | ba = zx, -z^2 + x^2 = a^2 - b^2 \Rightarrow -a * a + x^2 = z^2 - b^2 |
-7,905 | \tfrac{1}{-3 + i}*(i*4 - 2) = \frac{1}{-3 + i}*(i*4 - 2)*\dfrac{-i - 3}{-3 - i} |
53,155 | 130801 = 23 \cdot 5687 |
14,620 | |-(d*(-1))/h + z_0| = |\frac{1}{h} d + z_0| |
8,673 | k_1\cdot \dotsm\cdot k_t = k_t\cdot \dotsm\cdot k_1 |
6,201 | -d*(-1) + (-d) * (-d) * (-d) = -(-d + d^3) |
10,289 | \cos{\pi/2} + i \cdot \sin{\frac{\pi}{2}} = i |
-14,156 | (5 + 8 - 6\cdot 8)\cdot 2 = (5 + 8 + 48\cdot \left(-1\right))\cdot 2 = \left(5 - 40\right)\cdot 2 = \left(5 + 40\cdot \left(-1\right)\right)\cdot 2 = (-35)\cdot 2 = (-35)\cdot 2 = -70 |
21,474 | \mathbb{E}\left((Y_2 - Y_1)^2\right) = \mathbb{E}\left(Y_1^2 + Y_2^2 - 2*Y_1*Y_2\right) |
10,681 | z + 1/z = z + (-1) + 1 + \tfrac1z \geq (z + (-1))/z + 1/z + 1 |
-5,342 | 11/10000 = \dfrac{11}{10000} |
-23,255 | 1 - \frac174 = \frac37 |
-20,651 | \frac{(-18) p}{p*3 + 30 (-1)} = \frac{1}{p + 10 \left(-1\right)} ((-6) p) \frac33 |
14,675 | -14995\cdot 15190 + 6079\cdot 37469 = 1 |
13,281 | π = 3 + (6 + \frac{3^2}{6 + \tfrac{5^2}{6 + \dots}})^{-1} |
-8,036 | \dfrac{-5*i + 27}{5 - 2*i} = \frac{1}{5 - 2*i}*\left(27 - 5*i\right)*\frac{5 + 2*i}{5 + 2*i} |
34,753 | \sin\left(\tau\cdot 2\right) = 2\cos\left(\tau\right) \sin(\tau) |
32,968 | \frac{x+1}{x^{2}-x+1}=\frac{x-1/2+3/2}{x^{2}-x+1}=\frac{x-1/2}{x^{2}-x+1} +\frac {3/2}{x^{2}-x+1} |
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