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15,460 | -\int_1^x \cdots\,\mathrm{d}x = \int_x^1 \cdots\,\mathrm{d}x |
16,262 | h = x\cdot t \implies \bar{h} = \bar{x}\cdot t |
20,398 | \int_1^0 \cdots = -\int_0^1 \ldots |
4,672 | x^{-2.5} = \frac{1}{x^3}\sqrt{x} |
24,645 | x^{1/2}/x = \frac{x^{1/2}}{x^{1/2}\times x^{1/2}} = \frac{1}{x^{1/2}} |
-1,767 | \frac{5}{6} \cdot \pi = \pi \cdot 19/12 - \pi \cdot 3/4 |
-10,396 | \frac{4}{4}\cdot \left(-\frac3x\right) = -\dfrac{12}{x\cdot 4} |
8,943 | 2 - \mathbb{E}[W] = \mathbb{E}[-W + 2] |
13,182 | ( x^2, x \cdot y) = \left( x^2, x\right) \cap ( x^2, y) = x \cap ( x^2, y) |
22,099 | 8 = \frac13 \cdot (3 \cdot \left(-1\right) + 27) |
-20,264 | -6/5 \cdot \frac{6 - 4 \cdot N}{6 - N \cdot 4} = \frac{1}{30 - 20 \cdot N} \cdot (N \cdot 24 + 36 \cdot (-1)) |
-16,566 | 9 \times (16 \times 13)^{1 / 2} = 9 \times 208^{1 / 2} |
12,372 | \frac{\pi}{6} = \operatorname{atan}\left(1/(\sqrt{3})\right) |
-14,125 | \frac{2}{10 + 9 (-1)} = 2/1 = \dfrac21 = 2 |
19,938 | g + x = (g + x) \cdot (g + x) = g^2 + g \cdot x + x \cdot g + x^2 = g + g \cdot x + x \cdot g + x |
11,005 | (2 \cdot x + 1) \cdot \left(2 \cdot x + (-1)\right) + m \cdot 4 + 1 = 4 \cdot (x^2 + m) |
-2,171 | 35/12\cdot π = π\cdot 17/12 + π\cdot \dfrac{3}{2} |
-20,219 | \dfrac{1}{56 + 8 \cdot s} \cdot (s + 7) = \tfrac{1}{8} \cdot 1 |
19,524 | \frac{3*\frac14*3}{1} = 9/4 |
12,393 | 1 - z_1 \cdot z_2 = -(1 - z_2) \cdot (1 - z_1) + 1 - z_1 + 1 - z_2 |
102 | \sqrt{2} \cdot (-a)^{1/4} = 2^{\frac{1}{4}} \cdot 2^{\frac{1}{4}} \cdot (-a)^{\frac{1}{4}} = (-4 \cdot a)^{\frac{1}{4}} |
20,856 | Y^x\cdot Y\cdot Y^x\cdot Y\cdot Y^x\cdot Y = Y\cdot Y\cdot Y^x\cdot Y^x\cdot Y\cdot Y^x |
-18,464 | 60/45 = \frac{4}{3} |
7,320 | (2*a + 1)*\left(2*h + 1\right) = 4*a*h + 2*a + 2*h + 1 = 2*(2*a*h + a + h) + 1 |
10,527 | 4\cdot d\cdot b = (b + d) \cdot (b + d) - (-b + d)^2 |
20,556 | z^k = (z + 1) \cdot z \cdot \cdots \cdot ((-1) + z + k) |
36,889 | \sin\left(6x\right) = \sin\left(3*2x\right) = 3\sin(2x) - 4\sin^{32}(x) = \sin\left(2x*(3 - 4\sin^{22}(x))\right) |
-20,235 | \frac{90*R + 50}{-R*20 + 40*(-1)} = 10/10*\frac{9*R + 5}{-2*R + 4*(-1)} |
773 | 16*(-|C*A| + |G_2*G_1|) = 64\Longrightarrow |G_1*G_2| + 4*(-1) = |A*C| |
-9,324 | 72 - 40*q = -2*2*2*5*q + 2*2*2*3*3 |
3,913 | 3/2\cdot Q = n + \dfrac23 rightarrow Q = n\cdot \tfrac23 + \left(\frac{1}{3}\cdot 2\right)^2 |
18,856 | \left(8^2 + 5 \cdot 5\right) (13 \cdot 13 + 7 \cdot 7) = (8 \cdot 13 + 5 \cdot 7)^2 + (8 \cdot 7 - 5 \cdot 13)^2 = 139^2 + 9^2 |
15,429 | 5x^2 - w \cdot w = (-w + x \cdot 3) \cdot (-w + x \cdot 3) + (w - x) \left(3x - w\right) - \left(w - x\right)^2 |
603 | \frac{z^2}{3} - \frac{1}{3} = 1 + \dfrac13 \cdot (4 \cdot \left(-1\right) + z \cdot z) |
14,994 | S \cdot S^2\cdot U\cdot U^T\cdot S^3 = S^3\cdot U^T\cdot U\cdot S^3 |
23,698 | \frac{\binom{6}{3}}{6^3} = \frac{20}{216} = \dfrac{1}{54} \cdot 5 |
-4,301 | \dfrac{1}{z^3} \cdot z^2 = \frac{z \cdot z}{z \cdot z \cdot z} = 1/z |
10,115 | 60 = 4\cdot ((-1) + 16) |
24,987 | x + 0 \cdot (-1) = x + 0 \cdot (-1) + 0 |
15,141 | 16*n^4 = -(-1)^4 + 1 + (2*n)^4 |
32,536 | \frac{1}{4}\cdot (106 + 2\cdot \left(-1\right)) = 26 |
2,618 | A^2 - B \cdot B = (A - B) \cdot (B + A) |
9,457 | (5 + 2*\epsilon)*\left(5*\epsilon + 2\right) = \epsilon^2*10 + \epsilon*29 + 10 |
-4,026 | x^2/3 = \dfrac{x^2}{3} |
7,569 | |(z + (-1)) \cdot (2 \cdot (z + 1) + 3) + 3| = \ldots = |(z + \left(-1\right)) \cdot (2 \cdot z + 5) + 3| = |(z + (-1)) \cdot (2 \cdot z + 2 \cdot (-1) + 7) + 3| = |z + (-1)| \cdot (2 \cdot |z + (-1)| + 7) + 3 |
8,667 | \left(\left(-1\right) + \sqrt{2}\right) f*2 = (\sqrt{2} + (-1)) f*2 |
27,059 | \binom{6}{4} \times \binom{5}{1} \times \binom{5}{1} \times \binom{6}{4} = 5625 |
45,804 | \tfrac43 = 4/3 |
5,399 | \dfrac{1}{fx} = 1/(fx) |
14,894 | (x + 1)\cdot x + x = x\cdot 2 + x^2 |
-4,803 | 0.69\cdot 10^2 = 10^{4 + 2\cdot (-1)}\cdot 0.69 |
23,085 | 90 = {6 \choose 2}\cdot {2 \choose 2}\cdot {4 \choose 2} |
11,509 | 3\cdot x\cdot \cos{z \cdot z^2}\cdot y'\cdot z^2 + \sin{z^3} = x^2\cdot z\cdot \cos{x \cdot x \cdot x}\cdot 3 + \sin{x^3}\cdot y' |
24,144 | 2^{n + 5(-1)} = 2 \cdot 2^{n + 6\left(-1\right)} |
36,752 | 2*\left(x - j\right) = -(1 + 2*j) + 2*x + 1 |
4,656 | \frac{1}{10} \cdot \left(3018 + 18 \cdot \left(-1\right)\right) = 300 |
-9,158 | -7 \cdot k + 49 \cdot \left(-1\right) = -k \cdot 7 - 7 \cdot 7 |
-4,181 | 3\cdot \frac{1}{4}/r = 3/(4\cdot r) |
11,107 | 1 - 5 \cdot x^4 = -(5 \cdot x^4 + \left(-1\right)) = -(\sqrt{5} \cdot x^2 + (-1)) \cdot (\sqrt{5} \cdot x^2 + 1) |
29,992 | \left(a + 1\right)^2 - a^2 = a^2 + 2\cdot a + 1 - a^2 = 2\cdot a + 1 |
-9,671 | 6\% = \frac{6}{100} = 3/50 |
2,177 | m\cdot (m + 2(-1)) \ldots\cdot 3 = (m!)! |
-10,392 | -\frac{180}{100 + 20*y} = -\frac{9}{5 + y}*\frac{20}{20} |
-28,729 | y^2 - 14*y + 58 = y^2 - 14*y + 49 + 9 = (y + 7*(-1))^2 + 9 = (y*(-7))^2 + 3^2 |
-1,283 | \frac{1}{7 \cdot 1/5}(\frac{1}{2} (-7)) = -\frac{1}{2}7 \cdot \tfrac{5}{7} |
-20,580 | \frac{x\cdot 5 + 15 (-1)}{10 (-1) + 10 x} = 5/5 \frac{1}{2x + 2(-1)}(x + 3(-1)) |
-8,761 | 10 * 10 = 100 |
15,980 | 5/2 = \tfrac{2 + 3}{1 + 1} |
17,552 | \binom{l}{s} = \binom{l + (-1)}{s + (-1)} + \binom{(-1) + l}{s} |
30,022 | \frac{\frac12\cdot \left(-1\right)}{x + 1} + \frac{\frac{1}{2}}{x + (-1)} = \frac{1}{((-1) + x)\cdot (1 + x)} |
39,734 | \dfrac{12}{27} = \frac{3*2*4^2}{6^3} |
-19,722 | \dfrac15 \cdot 12 = \frac45 \cdot 3 |
23,848 | 1 + b^8 - 12 \cdot b^6 + b^4 \cdot 38 - b^2 \cdot 12 = (1 + b^4 - b^2 \cdot 6)^2 |
32,952 | \frac{1}{3}*4 = \frac43 |
-6,484 | \frac{1}{(y + 5)\cdot 3}\cdot 2 = \frac{2}{y\cdot 3 + 15} |
27,327 | x \cdot f \cdot x = x \cdot x \cdot f = x \cdot f |
12,935 | 4 \cdot y^3 - 7 \cdot y + 3 \cdot (-1) = (y + 1) \cdot (a \cdot y^2 + g \cdot y + f) = a \cdot y^3 + g \cdot y^2 + f \cdot y + a \cdot y^2 + g \cdot y + f |
19,140 | 1 + \frac{1}{1 + m} = \dfrac{2 + m}{1 + m} |
-19,088 | 44/45 = A_r/(81\cdot π)\cdot 81\cdot π = A_r |
-20,797 | \frac{1}{9\cdot r + 6}\cdot (-9\cdot r + 6\cdot (-1)) = -1^{-1}\cdot \frac{9\cdot r + 6}{9\cdot r + 6} |
6,135 | y^2 + 6 \cdot y + 8 = (y + 2) \cdot (4 + y) |
-18,404 | \frac{(x + 4)\times x}{(1 + x)\times (x + 4)} = \frac{x^2 + x\times 4}{x^2 + 5\times x + 4} |
4,754 | \frac53\cdot 2 = \frac{10}{3} |
-19,303 | \frac{\dfrac{1}{7}\cdot 9}{9\cdot \frac17} = \frac{1}{7}9\cdot \dfrac{1}{9}7 |
-4,408 | -\frac{1}{4\left(-1\right) + x} + \frac{5}{x + 2(-1)} = \frac{1}{8 + x^2 - x*6}(4x + 18 (-1)) |
23,320 | 2^{\frac{1}{3}} \cdot 2^{\frac{1}{3}}\cdot \left(3^{1/3}\right)^2 = (6^{\frac{1}{3}})^2 |
30,879 | \sin(\theta \cdot 2) = 2 \cdot \cos\left(\theta\right) \cdot \sin(\theta) |
-20,432 | \frac{5 - 35 s}{s*28 + 4(-1)} = -5/4 \frac{s*7 + (-1)}{(-1) + s*7} |
23,485 | \left(7 + x\right) \cdot 2 + x \cdot 3 + 14 (-1) = x \cdot 5 |
36,831 | d\cdot b = d\cdot b\cdot d^i\cdot d^{-i} = d\cdot d^i\cdot b\cdot d^{-i} = d^{i + 1}\cdot b\cdot d^{-i} = b\cdot d^{i + 1}\cdot d^{-i} = b\cdot d |
10,590 | y^3 + \frac{1}{y \cdot y^2} = (y + \frac1y) \cdot \left(\frac{1}{y} + y\right)^2 - 3\cdot (y + 1/y) |
-19,020 | 29/40 = \frac{X_r}{25 \cdot \pi} \cdot 25 \cdot \pi = X_r |
8,381 | \tan{z} = \frac{\sin{z}}{\cos{z}} = i*\frac{e^{-i*z} - e^{i*z}}{e^{i*z} + e^{-i*z}} |
-1,164 | -\frac{21}{56} = \tfrac{(-21)\cdot \frac{1}{7}}{56\cdot 1/7} = -3/8 |
14,583 | -2 \cdot z \cdot g - \int (-2 \cdot g)\,\mathrm{d}z = -2 \cdot g \cdot z + 2 \cdot \int g\,\mathrm{d}z = -2 \cdot g \cdot z + 2 \cdot g |
23,611 | 6 + 8*l = 2*(4*l + 3) |
43,621 | 300 \cdot 100 \cdot 99 \cdot 99 + 300 + 300 \cdot 100 + 300 \cdot 100 \cdot 99 = 297030300 |
-20,350 | \dfrac{1}{3} \cdot 1 = \frac{3 \cdot (-1) - n \cdot 3}{9 \cdot (-1) - n \cdot 9} |
21,392 | \tan{x} = \frac{2*\tan{\frac{x}{2}}}{1 - \tan^2{x/2}} \gt 2*\tan{x/2} |
27,372 | \frac{1}{1 - -y \cdot y} = \dfrac{1}{y^2 + 1} |
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