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4,002 | 4/243 = (\frac{1}{3} \cdot 2)^2 \cdot (\tfrac13)^3 |
-11,175 | (x + 8\cdot \left(-1\right))^2 + b = \left(x + 8\cdot (-1)\right)\cdot (x + 8\cdot (-1)) + b = x^2 - 16\cdot x + 64 + b |
7,229 | 1 = \lim_{n \to \infty}(1 + 1/n) = \lim_{n \to \infty}\left(1 + \frac{1}{n}\cdot 2\right) |
12,787 | a * a = (a + 12)*(a + 6) \Rightarrow a = -4 |
-19 | -8 = 3\cdot \left(-1\right) - 5 |
29,113 | 25*t^2 - 16*r^2 = (5*t)^2 - (4*r) * (4*r) = (5*t - 4*r)*(5*t + 4*r) |
-8,579 | 3/2 - 6/12 = 3\cdot 6/\left(2\cdot 6\right) - 6/(12) = \frac{1}{12}\cdot 18 - \frac{6}{12} = \tfrac{1}{12}\cdot (18 + 6\cdot (-1)) = \dfrac{12}{12} |
8,149 | 2(1 + x) = 2x + 2 |
12,712 | x!*(1 + x)*(x + 2) + \left(-1\right) = \left(-1\right) + x!*\left(2 + x\right)*(1 + x) |
26,038 | \pi + \tfrac18\pi*3 = \pi*11/8 |
11,896 | \left(1 - y + y^2/2! + \dots + \left(-1\right)\right) * \left(1 - y + y^2/2! + \dots + \left(-1\right)\right) = \left(e^{-y} + (-1)\right)^2 |
-10,463 | \frac{1}{8z}(z*4 + 20) = 2/2 (10 + z*2)/\left(4z\right) |
-24,267 | \frac{42}{2 + 5} = \frac{42}{7} = \dfrac17*42 = 6 |
-19,379 | \frac29 \times \dfrac35 = \frac{\frac19}{\tfrac{1}{3} \times 5} \times 2 |
-9,133 | -2*2 - a*2*2*3*3 = -36*a + 4*(-1) |
6,055 | V \cdot z \cdot x \implies x \cdot V \cdot z |
25,476 | 11/45 = 2/15 + \tfrac{1}{9} |
12,029 | \tan(d) = \frac{\sin(d)}{\cos(d)} = \frac{\sin\left(d\right)}{(1 - \sin^2(d))^{\dfrac{1}{2}}} |
-22,206 | a^2 - a \cdot 12 + 20 = \left(a + 2 (-1)\right) \left(a + 10 (-1)\right) |
14,243 | ac/(xb) = \frac1ba c/x |
-4,456 | x \cdot x + 2\cdot x + 3\cdot (-1) = ((-1) + x)\cdot (3 + x) |
-10,646 | \frac{18}{45 + 15 \cdot p} = 3/3 \cdot \dfrac{6}{p \cdot 5 + 15} |
5,991 | 1 + (1 + x) ((-1) + x) = x x |
30,635 | \frac16*255 = 85/2 |
19,423 | t = h - t^3 + h^3 \Rightarrow 0 = h - t + \left(-t + h\right) \times (h \times h + h \times t + t \times t) |
35,668 | 2\cdot Y = Y + Y |
2,258 | 2 \cdot \frac12 \cdot l = l |
7,212 | e^{|-x + y| + 1} = e^{|-x + y|}\cdot e^1 |
-893 | \dfrac{9265}{10000} = 0 + \frac{9}{10} + 2/100 + \dfrac{6}{1000} + 5/10000 |
-29,103 | 5\left(-9\right) = -45 |
-8,557 | 8/3 - \frac26 = \frac{8 \cdot 2}{3 \cdot 2} - \frac{2}{6} = \frac{16}{6} - \frac16 \cdot 2 = \frac16 \cdot (16 + 2 \cdot (-1)) = 14/6 |
-9,784 | -0.2 = -2/10 = -\frac{1}{5} |
-7,409 | \frac{1}{13} = \frac{6}{13} \cdot 2/12 |
20,213 | (5^a)^2 = 676 = 5^{2 \times a} |
4,699 | u = -a + x, y - a = v, w = z - a \implies a = x - u = y - v = z - w |
33,385 | \cos^4(y) = \cos^2(y)*\cos^2(y) |
-2,923 | ((-1) + 2)\cdot \sqrt{5} = \sqrt{5} |
-24,188 | \frac{85}{9 + 8} = \frac{1}{17}\cdot 85 = \frac{85}{17} = 5 |
12,723 | a*b*a = a*a*b |
31,882 | 12 = 4 \cdot s \Rightarrow s = 3 |
-19,153 | 17/40 = A_t/(25*\pi)*25*\pi = A_t |
-12,171 | 19/72 = \frac{1}{18\cdot \pi}\cdot q\cdot 18\cdot \pi = q |
25,669 | {52 \choose 5} = 52 \cdot 51 \cdot 49 \cdot 48 \cdot 50/5! |
40,071 | \pi = 2\pi/2 |
21,200 | \frac{1}{1 - p} p = \tilde{\pi} = (1 - p) \tilde{\pi}*2 |
19,215 | x^{1/r} = x^{1/r} |
-22,302 | 18 + z^2 - z\cdot 11 = (z + 2\cdot (-1))\cdot (z + 9\cdot \left(-1\right)) |
16,822 | -e^x\cdot 4 = (\frac{dx}{dt})^2\Longrightarrow i\cdot e^{x/2}\cdot 2 = \frac{dx}{dt} |
15,033 | \frac{\pi \cdot 9^2}{\pi \cdot 50^2} = 0.0324 |
-25,470 | \frac{d}{dx} (\cos{x} - x\cdot 7) = -\sin{x} + 7\cdot (-1) |
29,369 | (1 + x)^n\cdot \left(1 + x\right)^n = (x + 1)^{2\cdot n} |
4,105 | 3 \times \int\limits_0^{π/2} 1\,\mathrm{d}x = \int\limits_0^{\dfrac32 \times π} 1\,\mathrm{d}x |
4,443 | 4*2^{t + 2(-1)} = 2^t |
-20,214 | -\frac{8}{24\cdot \left(-1\right) - 28\cdot x} = 4/4\cdot (-\frac{1}{6\cdot (-1) - x\cdot 7}\cdot 2) |
6,140 | 3^{1/2}/3 = 1.73205081\cdot .../3 |
12,111 | \sin(\pi - e - f_1 - f_2) = \sin(e + f_1 + f_2) = \sin(e + f_1) \cdot \cos{f_2} + \cos(e + f_1) \cdot \sin{f_2} |
6,080 | z^3/2 - k\cdot z^2 + 4\cdot k\cdot z + 32\cdot (-1) = 1/2\cdot (z \cdot z^2 + 64\cdot (-1) - 2\cdot k\cdot z^2 + 8\cdot k\cdot z) = \frac12\cdot (z + 4\cdot \left(-1\right))\cdot (z^2 + 4\cdot z + 16 - 2\cdot k\cdot z) |
33,864 | \sum_{i=0}^{k+1}\binom{k+1}{i}= \sum_{i=0}^{k+1}\binom{k}{i}+\binom{k}{i-1}= \sum_{i=0}^{k}\binom{k}{i}+\sum_{i=1}^{k+1}\binom{k}{i-1}= 2\sum_{i=0}^{k}\binom{k}{i} |
10,129 | q\cdot X = q\cdot B = n \implies B\cdot X\cdot q = n |
-1,600 | \tfrac{19}{12} \pi = 2 \pi - \dfrac{5}{12} \pi |
38,711 | 0 \cdot 0^2 + 1^3 = 1^3 |
-531 | \pi \cdot 2/3 = 32/3 \pi - \pi \cdot 10 |
15,092 | \frac{b}{c^4} = \frac{b}{c^4} |
7,227 | h_1\cdot x = x\cdot h_1 |
43,916 | 2^{16} = (2^4)^4 = 16^4 |
-1,120 | -\frac82 = \frac{(-8) \frac12}{2\cdot 1/2} = -4 |
16,456 | \binom{10}{2} \cdot 8! = 10!/2! |
29,762 | 210\cdot x + 1100\cdot (-1) \Rightarrow \frac{1}{210}\cdot 1100 = x |
37,614 | z_1 + z_2 + z_3 = -z_3 + z_1 + z_2 + z_1 + z_3 + z_2 + z_3 - z_1 - z_2 |
14,224 | g\cdot x\cdot c = \frac{1}{x}\cdot g\cdot c = g\cdot 1/x/c = g/\left(x\cdot c\right) |
34,035 | y_2\cdot y_3\cdot y_1\cdot 3 = y_1\cdot y_2\cdot y_3 + y_2\cdot y_3\cdot y_1 + y_1\cdot y_2\cdot y_3 |
206 | \epsilon\cdot \sigma + \sigma\cdot z + \epsilon\cdot z = \epsilon\cdot \sigma\cdot z\cdot (\dfrac1z + \tfrac{1}{\epsilon} + \tfrac{1}{\sigma}) |
8,790 | (-b + a) \cdot (-b + a) \cdot 4 = 4 \cdot b^2 - 8 \cdot b \cdot a + a^2 \cdot 4 |
13,495 | (y + 4 \cdot (-1))/2 \cdot 2 = 4 \cdot (-1) + y |
6,618 | v - 1/v = -\frac{1}{x} + x \Rightarrow v - x = -1/x + 1/v |
53,046 | n = (-550 + (550^2 - 200 \cdot \left(500 - b_n\right))^{1/2})/100 = (-55 + (55^2 - 2 \cdot (500 - b_n))^{1/2})/10 = (-55 + (2025 + 2 \cdot b_n)^{1/2})/10 |
-5,248 | 10^1*18.8 = 18.8*10^{-4 + 5} |
-21,052 | \tfrac48 = \tfrac{2}{4}\cdot 2/2 |
12,832 | \frac{1}{8*9} = 1/72 |
-1,741 | \frac{7}{12}*\pi + \pi*\frac{19}{12} = \frac{13}{6}*\pi |
1,070 | h \cdot r + z^2 - (h + r) \cdot z = (-r + z) \cdot (z - h) |
34,321 | \left(z + I\right) (z + 1 + I) = z \cdot z + z + I = z^2 + 1 + z + (-1) + I = z + 1 + I |
-30,282 | \dfrac{1}{2\cdot (-1) + x}\cdot 7 + x + (-1) = \frac{1}{2\cdot (-1) + x}\cdot (x^2 - x\cdot 3 + 9) |
44,594 | 6 = (a + b) + \left(b + c\right) + \left(a + c\right) \leq \sqrt{1^2 + 1^2 + 1 \cdot 1} \cdot \sqrt{(a + b)^2 + \left(b + c\right)^2 + (a + c) \cdot (a + c)} |
-2,728 | (1 + 2\cdot (-1) + 5)\cdot \sqrt{11} = 4\cdot \sqrt{11} |
30,362 | (-r + 1) (1 + r) = 1 - r \cdot r |
-2,223 | -\dfrac{1}{14} + \frac{7}{14} = \dfrac{6}{14} |
-25,586 | \frac{3}{s \cdot s} = \frac{\mathrm{d}}{\mathrm{d}s} \left(-3/s\right) |
-20,900 | \tfrac{-y\cdot 4 + 16}{y\cdot 18 + 72\cdot (-1)} = -2/9\cdot \dfrac{2\cdot y + 8\cdot (-1)}{2\cdot y + 8\cdot (-1)} |
-10,610 | 5 = -8 - 3\cdot x + 6 = -3\cdot x + 2\cdot \left(-1\right) |
30,754 | k {8 \choose k} = 8 \frac{7!}{(k + (-1))! (7 - k + (-1))!} = 8 {7 \choose k + (-1)} |
-22,310 | n \cdot n - n\cdot 2 + 80\cdot \left(-1\right) = \left(8 + n\right)\cdot (n + 10\cdot \left(-1\right)) |
21,251 | z^2 + 5 \cdot z + \left(-1\right) = (3 \cdot \binom{z}{1} + \binom{z}{2}) \cdot 2 + (-1) |
-11,942 | 9.801\times 0.1 = \tfrac{1}{10}\times 9.801 |
-16,229 | \frac{1}{64} = \dfrac{1}{64} |
9,935 | \frac{1}{l}*{l \choose x} = \frac{(l + (-1))!}{x!*(l - x)!} = \frac1x*{l + \left(-1\right) \choose x + \left(-1\right)} |
2,141 | ( x, e) \cdot ( f, \zeta) = \left( x, e, 0\right) \cdot \left( f, \zeta, 0\right) = \left( 0, 0, x \cdot \zeta - e \cdot f\right) |
7,906 | (n + m)*(n - m) = n * n - m * m |
29,350 | (z - g) \cdot \left(-g + z\right) = \left(-g + z\right)^2 |
17,449 | \left(1 \leq 0 \Rightarrow 1 = 0,2 \leq 0\right) \Rightarrow 0 = 2,... |
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