id
int64 -30,985
55.9k
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14,278 |
\binom{1 + m}{x} = \binom{m}{x} + \binom{m}{x + (-1)}
|
-20,324 |
-\frac12*3*\frac{4*(-1) + x}{4*(-1) + x} = \tfrac{1}{8*(-1) + 2*x}*(12 - 3*x)
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21,614 |
1 + 25 w^2 - 10 w = (5 w + (-1))^2
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15,082 |
\frac{1}{e^{bx} + 1} = \frac{e^{-xb}}{e^{-xb} + 1}
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-9,144 |
z \cdot z \cdot 2 \cdot 2 \cdot 5 = z^2 \cdot 20
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21,147 |
(k + 1)^{k + 1} = (1 + k)^k \cdot \left(k + 1\right)
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25,538 |
2 \cdot (x^2 - 3 \cdot x + 1) + x \cdot 7 + (-1) = 1 + x^2 \cdot 2 + x
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-3,044 |
4^{1/2}\cdot 7^{1/2} + 9^{1/2}\cdot 7^{1/2} = 3\cdot 7^{1/2} + 7^{1/2}\cdot 2
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19,615 |
12 = {4 \choose 3} \cdot 3
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6,288 |
\cos(2 \cdot x/2) = \cos(x)
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-12,895 |
8 + 8 + 7 = 23
|
-7,956 |
\frac{1}{-i - 2}\cdot (-2 - i)\cdot \dfrac{1}{i - 2}\cdot (8 + i) = \dfrac{1}{i - 2}\cdot (8 + i)
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-1,450 |
-5/45 = \left((-5)*\frac15\right)/(45*\frac{1}{5}) = -1/9
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26,135 |
(c + d)^2 - (-g^2 + d \cdot c) \cdot 4 = g \cdot g \cdot 4 + (d - c)^2
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4,863 |
\sin\left(b + a\right) = \sin{a} \cos{b} + \cos{a} \sin{b}
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28,533 |
\cos\left(2*D\right) = 2*\cos^2(D) + (-1)
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21,959 |
52 \frac{(-1) + 98^4}{(-1) + 98} = 9944*9945/2
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13,274 |
\frac{1}{2^2} = \frac{1}{2^2}\cdot 2^0 = \dfrac14
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26,022 |
\int 1/\left(\sqrt{z}\right)\,\mathrm{d}z = \int z^{-\dfrac12}\,\mathrm{d}z
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14,914 |
(x + b)^{1 + n} = (b + x)*(b + x)^n
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16,921 |
10 \cdot x = \dfrac{1}{-2} \cdot \left(\left(-20\right) \cdot x\right) = -0.5 \cdot \left(-20 \cdot x\right)
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-23,348 |
3/4 \cdot \frac49 = \dfrac{1}{3}
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-15,150 |
\frac{1}{(d^4 x^2)^5 x} = \frac{1}{d^{20} x^{10} x}
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11,293 |
-35 \cdot (f + a \cdot y) - 2 \cdot a = -35 \cdot a \cdot y - a \cdot 2 + f \cdot 35
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21,275 |
\left(1 + l\right)! = \left(l + 1\right)*l*...*2
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6,860 |
\left(-1\right)^{\tfrac{1}{2}} + \frac{1}{1/2} = (-1)^{1/2} + 2 = 2 + i
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16,358 |
2^{7.16} = 2^{716/100} = \sqrt[100]{2^{716}}
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3,824 |
\mathbb{E}(\bar{X})^2 + Var(\bar{X}^2) = \mathbb{E}(\bar{X}^2)
|
-18,979 |
\frac29 = \frac{1}{36 \cdot \pi} \cdot A_s \cdot 36 \cdot \pi = A_s
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-1,502 |
-\frac92*\frac{9}{2} = ((-1)*9*\frac12)/\left(2*1/9\right)
|
913 |
\sin{C} \cdot \cos{C} \cdot 2 = \sin{2 \cdot C}
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-19,591 |
\dfrac{1/6 \cdot 5}{1/7 \cdot 6} = 7/6 \cdot 5/6
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18,380 |
\left(b + a\right) \cdot (a + b) \cdot \left(b + a\right) = (b + a)^3
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-4,200 |
27/54 \frac{x^4}{x^5} = \dfrac{x^4 \cdot 27}{x^5 \cdot 54}
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7,198 |
\frac{\text{d}}{\text{d}x} \sin^2{3 x} = 2 \sin{3 x} \cos{3 x}*3 = 6 \sin{3 x} \cos{3 x}
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10,857 |
\dfrac{1}{6^2}(6^2 - 1^2) = 1 - \frac{1}{36}
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-26,628 |
9m^2+30mn+25n^2=(3m+5n)^2
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37,207 |
4! \times 3 \times 5! = 8640
|
13,073 |
C*E = x_n \Rightarrow E*C = x_n
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11,423 |
\tan(\arctan(y) + \arctan\left(y^3\right)) = \frac{1}{1 - y^4}\times (y + y \times y \times y) = \frac{y}{1 - y^2}
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43,751 |
416965528 = {140 \choose 5}
|
165 |
4 + n*21 = \left(n*14 + 3\right) + n*7 + 1
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10,305 |
\left(g + b = b\cdot g \implies b\cdot g - g - b = 0\right) \implies (b + (-1))\cdot ((-1) + g) = 1
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-5,734 |
\dfrac{3}{10*(-1) + t*5} = \frac{3}{5*(2*(-1) + t)}
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-25,894 |
6.75 = 27/4
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-20,206 |
\frac77 \dfrac{7(-1) + f}{f + \left(-1\right)} = \frac{7f + 49 (-1)}{7f + 7(-1)}
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-15,678 |
\frac{(\frac{1}{z^5})^2}{1/n\cdot \frac{1}{z \cdot z}} = \frac{1}{z^{10}\cdot \frac{1}{n\cdot z^2}}
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-13,232 |
\frac{1}{-0.0009}*0.000243 = -0.27
|
9,811 |
\dfrac{1}{4 \cdot 5} = -\frac15 + \dfrac{1}{4}
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5,104 |
a + b\times \omega + c\times \omega^2 = a + b\times \omega - c\times \left(1 + \omega\right) = a - c + (b - c)\times \omega
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22,898 |
-\tfrac{1}{2} = \dfrac{1}{-\sqrt{1} + (-1)}
|
5,306 |
q + 1 = 0\Longrightarrow q = -1
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15,357 |
4ua = q^2 \Rightarrow q^2 = au*4
|
31,391 |
\sin{z}\cdot \cos{z} = \sin{z}\cdot \sin(\frac{\pi}{2} - z)
|
-19,013 |
\dfrac12 = \frac{A_s}{16\cdot \pi}\cdot 16\cdot \pi = A_s
|
-1,833 |
\frac{7}{6} π = 2/3 π + \dfrac{π}{2}
|
-11,495 |
i*3 + 1 + 4 = 5 + 3*i
|
21,582 |
B \times B \times B + H^3 = \left(B^2 + H \times H - H\times B\right)\times (H + B)
|
-23,356 |
\frac{4}{21} = \frac{2}{7} \times \frac{2}{3}
|
35,794 |
\sin(x+\pi/2)=\cos x
|
26,133 |
1/4 = \frac{1}{2}\cdot (1^{-1} - 1/2)
|
14,931 |
G = A \cdot T \Rightarrow \frac{\mathrm{d}G}{\mathrm{d}A} = A \cdot \frac{\mathrm{d}T}{\mathrm{d}A} + T
|
-23,027 |
\frac{10}{9 \cdot 10} \cdot 7 = \dfrac{70}{90}
|
-28,818 |
\left(2 + 6\right)/2 = 8/2 = 4
|
1,753 |
\frac{1 - c^2}{1 - c} = c + 1
|
23,735 |
-(3 k + 4) + 0 = 0 \implies k = -4/3
|
-5,540 |
\dfrac{1}{(t + 2) \cdot 3} \cdot 5 = \frac{1}{6 + 3 \cdot t} \cdot 5
|
-22,839 |
\dfrac{21}{28} = 3\cdot 7/(4\cdot 7)
|
17,725 |
(a + b)^n = a^n + a^{n + \left(-1\right)}\cdot b\cdot {n \choose 1} + ...
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31,533 |
(3(-1) + 3^5)/5 = 48
|
11,875 |
9699 = 53 + \frac{1}{2}\cdot 19292
|
-11,499 |
2 i + 1 + 3 = 4 + i*2
|
11,470 |
\frac{1}{z \cdot 2} \cdot (2 + z) = \dfrac{z}{z \cdot 2} + \frac{2}{2 \cdot z}
|
17,415 |
-(x^2 + z^2) + (z + x) * (z + x) = xz*2
|
24,680 |
\mathbb{E}[x^2] = \mathbb{E}[x] \times \mathbb{E}[x] + \mathbb{Var}[x]
|
-3,070 |
8 \cdot 3^{1/2} = 3^{1/2} \cdot \left(1 + 5 + 2\right)
|
-4,407 |
\left(x + 3 \cdot \left(-1\right)\right) \cdot (4 \cdot (-1) + x) = x^2 - x \cdot 7 + 12
|
6,081 |
(x + \alpha\cdot y)^2 = x^2 + \alpha^2\cdot y^2 + x\cdot y\cdot \alpha\cdot 2
|
-430 |
e^{11 \pi i \cdot 7/6} = (e^{7\pi i/6})^{11}
|
26,456 |
E\left(X \cdot Y\right) = E\left(X \cdot X \cdot X\right) = 0 = E\left(X\right) \cdot E\left(Y\right)
|
-3,889 |
\dfrac43*z^3 = \frac{4*z^3}{3}
|
37,847 |
z\cdot e = z\cdot e
|
2,557 |
\tfrac{32}{144} = \dfrac29
|
22,926 |
G^c \cap (B \cap C) = G^c \cap \left(B \cap C\right) = C \cap (B \cap G^c) = C \cap (B \cap (G^c)) = \left(B \cap G^c\right) \cap (C \cap G^c)
|
21,482 |
\dfrac{(-2)^k}{3^{k + 1}} = \left(-2/3\right)^k/3
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-20,775 |
8/8*\frac{1}{x + 5*(-1)}*(-6*x + 2) = \frac{-48*x + 16}{40*(-1) + x*8}
|
-25,362 |
d/dz \cot(z) = -\frac{1}{\sin^2\left(z\right)}
|
-10,740 |
\frac{2*k + 9*(-1)}{k + 3}*4/4 = \frac{8*k + 36*(-1)}{4*k + 12}
|
17,522 |
2*3^2 + 3 \left(7/2\right) \left(7/2\right) = \frac{219}{4} \neq 17
|
35,153 |
247 + 127*(-1) = 120
|
17,747 |
\frac{1}{D^T D} = \dfrac{1}{DD^T}
|
31,429 |
1/C + \frac{1}{G} + 1/Z = (GZ + ZC + CG)/(CZ G)
|
13,432 |
x_1 + x_2 + \dots + x_{1 + n} = x_1 \cdot x_2 \cdot \dots \cdot x_{n + 1}
|
-2,742 |
5^{\dfrac{1}{2}} \cdot \left(4 + 5 \cdot \left(-1\right) + 2\right) = 5^{1 / 2}
|
-22,272 |
15\cdot (-1) + a^2 + a\cdot 2 = (a + 5)\cdot (3\cdot (-1) + a)
|
39,596 |
(f + (-1)) \cdot (f + (-1)) + \left(b + 1\right)^2 = f^2 + b \cdot b + 2\cdot (b + 1 - f) \leq f^2 + b^2
|
5,182 |
\frac{\partial}{\partial x} \left(e \cdot x\right) = \frac{dx}{dx} \cdot e + x \cdot \frac{de}{dx}
|
14,296 |
3 + b = a + 3 \Rightarrow b = a
|
36,266 |
2 \cdot 2^{k + (-1)} = 2^1 \cdot 2^{k + \left(-1\right)} = 2^{1 + k + (-1)} = 2^k
|
31,484 |
y^b \cdot y^a = y^{b + a}
|
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