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23,486 | \tfrac{6!}{3!} = 6\times 5\times 4 = 120 |
21,449 | \left(l + 1\right)^2 = l \cdot l + 2\cdot l + 1 \gt l^2 + 1 |
-10,937 | \dfrac{117}{9} = 13 |
-9,498 | 30 \cdot q + 5 = q \cdot 2 \cdot 3 \cdot 5 + 5 |
5,156 | (5 + b)^2 + 25\cdot (-1) = 25 + 10\cdot b + b^2 + 25\cdot (-1) = 10\cdot b + b^2 |
11,717 | 8 = a * a - f^2 = (a + f)*(a - f) |
-18,394 | \frac{z * z - 5*z}{z^2 - z*13 + 40} = \dfrac{\left(z + 5*\left(-1\right)\right)*z}{\left(5*(-1) + z\right)*(8*(-1) + z)} |
17,058 | v = w + u \Rightarrow w = -u + v |
369 | \dfrac{1}{\infty} = 2/\infty = 0 |
22,609 | \cos(x) = \cos(x + π\cdot 2) |
-4,817 | 10^2*3.1 = 3.1*10^{\left(-4\right) (-1) - 2} |
52,450 | 1 = \frac{1}{25} \cdot 25 |
21,975 | (1 + k)^2 + j - k + (-1) = k \cdot k + j + k |
4,997 | \frac{\sin\left(\lambda\right)}{\cos(\lambda)} = \tan(\lambda) |
-9,351 | -121 z^2 = -11*11 z z |
39,878 | g^2 + y^2 = y^2 + g^2 |
5,104 | d + b\cdot \omega + x\cdot \omega \cdot \omega = d + b\cdot \omega - x\cdot \left(1 + \omega\right) = d - x + (b - x)\cdot \omega |
20,264 | \frac{3}{2}*3 = 4.5 |
8,618 | 4 \times (-1) + (2 + n) \times (2 + n) = n^2 + n \times 4 |
30,216 | X^2 = X \cdot X = X |
9,602 | 1 + 2 + \ldots + x + x + 1 = \dfrac12 \cdot \left(x + 1\right) \cdot \left(x + 2\right) |
11,262 | 8\cdot x^2 - 20^x + 16 + ... = x^3 |
29,794 | a\cdot c\cdot a\cdot c\cdot a\cdot c\cdot a\cdot c\cdot c\cdot a = c^5\cdot a^5 |
11,099 | -(2a)^{1/3} \cdot 3 = -3 \cdot a^{\frac{1}{3}} \cdot 2^{1/3} |
-5,159 | 10^{6 + 2*(-1)}*0.81 = 0.81*10^4 |
32,220 | l = z*m \Rightarrow m = \frac{l}{z} |
23,402 | a\cdot b = \frac{b}{a} = b\cdot a^7 |
27,653 | \frac{1}{2!\cdot 1!}\cdot \left(2 + 1\right)! = 3 |
13,769 | r_1 \cdot x_1 + r_2 \cdot x_2 + r_3 \cdot x_2 + r_4 \cdot x_3 = x_1 \cdot r_1 + (r_3 + r_2) \cdot x_2 + r_4 \cdot x_3 |
-25,242 | \tfrac{1}{2\cdot 9^{1 / 2}} = 1/(2\cdot 3) = \frac{1}{6} |
-15,150 | \tfrac{1}{\left(k \cdot k\cdot a^4\right)^5\cdot k} = \dfrac{1}{k\cdot k^{10}\cdot a^{20}} |
27,255 | ac a = c = aca |
20,581 | b + a = -1\Longrightarrow a - b = -16 |
4,821 | 12/7 = 48/28 |
18,285 | 1 - \cos(x) = 2\sin^2(x/2) \leq \frac{x^2}{2} |
36,348 | -\sqrt{3} = -\frac{3}{\sqrt{3}} |
-18,525 | 3 \cdot z + 2 \cdot (-1) = 6 \cdot (2 \cdot z + 9 \cdot (-1)) = 12 \cdot z + 54 \cdot (-1) |
9,603 | \frac{d}{dy} e^{y*i} = e^{y*i}*i |
21,736 | x = n \cdot s \cdot \vartheta_1 + \vartheta_2 \cdot n \Rightarrow \vartheta_1 \cdot s + \vartheta_2 = x/n |
24,341 | p d/dx x^i + \frac{\partial}{\partial x} x^k s = s x^{k + (-1)} k + i x^{i + (-1)} p |
38,710 | \left(-1\right) + \psi_2 = \psi_2 |
19,299 | (2^n + 1)*(2^n + (-1)) = (-1) + 2^{2*n} |
25,088 | 0 = 1\cdot 0 + 0\left(-2\right)\cdot 3 + 0\cdot 0 |
-10,377 | 2/2 (-\frac{z + 6\left(-1\right)}{3(-1) + z}) = -\dfrac{1}{6(-1) + 2z}(12 (-1) + 2z) |
30,735 | 2^{-l} = 2^l\cdot 4^{-l} |
16,159 | \tfrac12*\left(3 + 6 + 9\right) + (3 + 9)/2 = 9 + 6 = 15 |
9,330 | (\sqrt{d} \cdot \sqrt{a}) \cdot (\sqrt{d} \cdot \sqrt{a}) = \left(\sqrt{d}\right)^2 \cdot \left(\sqrt{a}\right)^2 |
2,292 | \dfrac{1}{a_x + 1}*a_x = \frac{1/(a_x)*a_x}{\dfrac{1}{a_x} + 1} |
3,216 | 0 = d d \Rightarrow d = 0 |
36,412 | 2400 = \left(-1\right) + 7^4 |
2,390 | p = \frac{1}{\cos{x} - 4 \times \sin{x}} \times 4 \Rightarrow \cos{x} \times p - p \times \sin{x} \times 4 = 4 |
441 | \mathbb{E}\left[H\cdot X\right] = \mathbb{E}\left[H\right]\cdot \mathbb{E}\left[X\right] |
48,886 | \left(2 + 1\right)^2 = 3^2 |
-23,048 | 3/2\cdot \frac12\cdot 3 = 9/4 |
1,911 | 42 = 2 \cdot 84/17 \cdot \frac{1/2}{2} \cdot 17 |
27,920 | \dfrac12(789998 + 2) = 395000 |
47,689 | 3! \binom{4}{2} = 36 |
29,764 | \frac{1}{50}25 / 26 = \frac{1}{52} |
27,913 | \frac{3}{4} = \tfrac14\cdot \left(1 + 1 + 1\right) = \frac{1}{4} + 1/4 + 1/4 |
5,310 | z^{2\cdot s} - 2\cdot z^s + 1 = (z^s + (-1))^2 |
-13,217 | ((-4)*\tfrac{1}{3})/2 = \dfrac{1}{3*2}*\left((-4)\right) = -\frac46 |
32,014 | c \cdot \left(-f\right) + -c \cdot (-f) = -c \cdot \left(-f\right) - c \cdot f |
-6,687 | \frac{4}{10} + 4/100 = 40/100 + 4/100 |
-3,761 | \frac{1}{x^4} \times x^4 \times 35/15 = \frac{x^4 \times 35}{15 \times x^4} \times 1 |
31,052 | (1 + x^2)\times (x^4 + 1 - x^2) = 1 + x^6 |
3,105 | \cos\left(B\right)\cdot \sin(A) + \cos(A)\cdot \sin(B) = \sin\left(A + B\right) |
33,672 | \left(m + 2\right)! + \left(-1\right) = (m + 2)\times (m + 1)! + (-1) = (m + 2)\times (m + 1)\times m! + (-1) |
4,929 | \sqrt{5} + b = \left(\sqrt{\sqrt{5} + b}\right)^2 |
-6,682 | 20/100 + 9/100 = 2/10 + \tfrac{9}{100} |
40,412 | (2k + 1)^2 + 8 = 4k^2 + 4k + 1 + 8 = 2*(2k * k + 2k + 4) + 1 |
-5,048 | \frac{9.7}{1000} = \dfrac{1}{1000} \cdot 9.7 |
262 | 3\cdot z^3 - 3\cdot z + 9 = 3\cdot (z^3 - z + 3) = 3\cdot (z^2 + d\cdot z + h)\cdot (z + g) = z^3 + (g + d)\cdot z^2 + (d\cdot g + h)\cdot z + h\cdot g |
2,903 | 1 = 2 \cdot (x/z)^2 + \left(y/z\right)^2 \cdot 3 \Rightarrow z \cdot z = 2 \cdot x^2 + 3 \cdot y^2 |
23,935 | y^{12} + (-1) = \left(y^6 + 1\right)^2 = ((y^3 + 1) \cdot (y^3 + 1))^2 = (\left((y + (-1)) \cdot (y^2 + y + 1)\right)^2)^2 |
17,222 | \frac{1}{2^k} \cdot (2^k + \left(-1\right)) = \dfrac12 + \frac{1}{4} + \frac18 + ... + \frac{1}{2^k} |
13,749 | (a + b)^4 = a^4 + b*a^3*\binom{4}{1} + a * a*b * b*\binom{4}{2} + \binom{4}{3}*b^3*a + b^4 |
16,307 | e^{a + f} = e^a \times e^f |
25,827 | 1/40 + 1/10 = \frac{5}{40} |
33,352 | {6 \choose 2}*4! = 6!/(2!*4!)*4! = \frac{1}{2!}*6! = 360 |
3,058 | \dfrac{1}{2} \cdot (4 + 6) = 5 |
-518 | \left(e^{\frac32\pi i}\right)^{10} = e^{10*3\pi i/2} |
-19,675 | 25/8 = \dfrac{5\cdot 5}{8} |
-4,444 | -\frac{1}{3(-1) + x}2 - \frac{3}{1 + x} = \frac{7 - x*5}{x^2 - 2x + 3(-1)} |
32,662 | \frac{1}{3}\cdot 10 = \frac33 = 3\cdot 4/12 = 3.4 |
27,474 | i \cdot x \cdot 2 = 1 \implies x = \frac{1}{i \cdot 2} |
20,131 | 0 = a^4 + 1 = (a * a + 1)^2 - 2*a * a |
11,194 | z^2 + 6\cdot z + 9 = (3 + z)^2 |
24,671 | -2 \cdot a + x^2 + 2 \cdot x - a^2 = (x - a) \cdot 2 + x^2 - a^2 |
-17,422 | 14 = 16 + 2 \cdot (-1) |
3,027 | l\cdot \left(0.3 + 0.1\right) = l\cdot 0.4 |
-23,123 | -3/2 = -\frac{1}{2} \times 3 |
33,940 | e + m = e + m |
-22,602 | \left(\left(-6\right) \cdot 1/7\right)/9 = \dfrac{(-6)}{9 \cdot 7} = -\frac{1}{63} \cdot 6 = -2/21 |
16,005 | yx = ((x + y)^2 - y^2 + x \cdot x)/2 |
-18,544 | p + 9 = 5 \cdot (p + 4) = 5 \cdot p + 20 |
-19,147 | \tfrac{19}{24} = A_r/\left(36\cdot \pi\right)\cdot 36\cdot \pi = A_r |
11,383 | \dfrac13 = 1/(3\cdot 4) + 1/4 |
-3,997 | \frac{1}{x^5} \cdot x \cdot x \cdot x \cdot \tfrac{16}{2 \cdot 16} = \frac{16}{32} \cdot \tfrac{x^3}{x^5} |
8,553 | z \cdot z - 6 \cdot z + 12 = (z + 3 \cdot (-1)) \cdot (z + 3 \cdot (-1)) + 3 = (z + 3 \cdot (-1)) \cdot (z + 3 \cdot (-1)) + 3 |
27,491 | \frac{E}{C} + G/C = (E + G)/C |
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