id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
30,060 |
(x^2)^m = c \implies x^{2m} = c
|
-22,216 |
(t + 10) \cdot (t + 9) = t^2 + t \cdot 19 + 90
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12,110 |
\sin(x + \gamma) = \sin{\gamma} \cos{x} + \cos{\gamma} \sin{x}
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15,375 |
\frac{1}{64}\cdot 15 + \frac{6}{64} + 1/64 = 22/64
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-16,563 |
9\cdot \sqrt{16}\cdot \sqrt{13} = 9\cdot 4\cdot \sqrt{13} = 36\cdot \sqrt{13}
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11,523 |
y' \cdot 4 + x \cdot 2 + 2y' y + 6(-1) = 0 \implies y' = \frac{1}{2y + 4}(6 - 2x) = \dfrac{1}{y + 2}(3 - x)
|
33,174 |
(1 + \sqrt{-5}) (-\sqrt{-5} + 1) = 6
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7,016 |
\frac{d_1^{d_2}}{d_1^c} = d_1^{d_2 - c}
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-20,191 |
7/7 \cdot \frac{1}{9} \cdot (x + 3 \cdot (-1)) = \tfrac{1}{63} \cdot (7 \cdot x + 21 \cdot (-1))
|
6,536 |
x/4 + \frac{1}{4}*x + x/4 + \frac{x}{4} = x
|
8,500 |
\sin{\theta/2} \cdot \cos{\frac{1}{2} \cdot \theta} \cdot 2 = \sin{\theta}
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14,386 |
\frac{g*1/h}{1 - -\frac1h z y} = \frac{g}{h + z y}
|
26,928 |
\operatorname{asin}(\sin(\pi + 2\cdot (-1))) = \operatorname{asin}(\sin(2))
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-3,657 |
\dfrac{k^4}{k \cdot k \cdot k} = \frac{k\cdot k\cdot k\cdot k}{k\cdot k\cdot k} = k
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-1,458 |
-5/7 \cdot 8/7 = \frac{8 \cdot \frac{1}{7}}{(-1) \cdot 7 \cdot \frac{1}{5}}
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-11,566 |
19 i + 25 = 19 i + 10 + 15
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-20,236 |
\frac{4*(-1) - y*2}{-2*y + 4*\left(-1\right)}*(-\tfrac{1}{10}*3) = \frac{y*6 + 12}{-y*20 + 40*(-1)}
|
-509 |
\pi\cdot 323/12 - \pi\cdot 26 = \dfrac{1}{12}\cdot 11\cdot \pi
|
-3,921 |
\dfrac{r^2*84}{r^5*42} = \frac{r^2}{r^5}*84/42
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35,703 |
V_X = V_X^1
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11,028 |
(2^{1/2} \cdot z + (-1)) \cdot \left(1 + 2^{1/2} \cdot z\right) = (-1) + z^2 \cdot 2
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20,289 |
2 + 3 = 5 > 4
|
14,720 |
y/z = v \implies y = vz
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-6,209 |
\frac{1}{y^2 - y\cdot 10 + 25} = \frac{1}{(5\cdot (-1) + y)\cdot (y + 5\cdot (-1))}
|
-5,210 |
10^5 \cdot 7.1 = 10^{1 - -4} \cdot 7.1
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45,764 |
2.2 = \dfrac{11}{5}
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16,122 |
u^2 - v^2 = (u + v)\cdot \left(u - v\right)
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34,139 |
ax+bx=(a+b)x
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28,262 |
\frac16\cdot \sin(\pi) - \sin(0)/6 = 0 + 0\cdot (-1) = 0
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6,485 |
0*a - 0*a = a*0
|
11,478 |
\min{y, x'} = \frac12 \times \left(y + x' - |-x' + y|\right)
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-23,150 |
-4 = 3(-4/3)
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3,787 |
\frac{1}{y} = \frac{\overline{y}}{\overline{y} y}
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2,574 |
(h + b) c = cb + ch
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35,696 |
(-1) + y^3 = \left(y^2 + y + 1\right)\cdot ((-1) + y)
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39,532 |
h\cdot b\cdot b = b\cdot h\cdot b
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9,233 |
(2*(-1) + x)*\left(2 + x\right) = x^2 + 0*x + 4*(-1)
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-12,533 |
3 = \tfrac{30}{10}
|
8,415 |
k \cdot 0.25 \cdot (2 \cdot g)^2 = k \cdot g^2
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32,888 |
2017 = 2017*\sqrt{2 + \left(-1\right)}
|
8,539 |
4\cdot 1/27/180 = \frac{1}{1215}
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47,411 |
\frac{|\overline{CB}|}{\sin A} = \frac{|\overline{CA}|}{\sin B} = \frac{|\overline{AB}|}{\sin C} \quad \left(= \frac{a+b}{\sin(A+B)}\;\right)
|
-1,246 |
3 \times 1/2/(1/8) = \frac12 \times 3 \times 8/1
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47,255 |
6 + 3 = 5 + 4
|
9,455 |
k\cdot A = j\Longrightarrow A\cdot k = j
|
30,090 |
\tilde{x}\cdot b = \frac{0.036\cdot x}{0.0018\cdot b} = \dfrac{x}{b}\cdot 20
|
-2,500 |
2^{1 / 2}*(4 + 5 + 2*(-1)) = 7*2^{\frac{1}{2}}
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32,517 |
FF = FF
|
40,359 |
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)*99 = 5445
|
1,320 |
\frac1z\cdot \sin{z} = \left(z - \dfrac{1}{6}\cdot z \cdot z \cdot z + \dotsm\right)/z = 1 - \dfrac{z^2}{6} + \dotsm
|
46,396 |
3 \cdot 193 = 579
|
-4,427 |
\frac{-z*5 + 8*(-1)}{2 + z * z + 3*z} = -\frac{1}{z + 2}*2 - \dfrac{3}{1 + z}
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-15,597 |
\frac{1}{b^6\cdot x^6}\cdot b\cdot \frac{1}{x} = \dfrac{b\cdot \frac{1}{x}}{\frac{1}{\frac{1}{b^6}\cdot \frac{1}{x^6}}}
|
-10,602 |
\frac{8}{8\cdot (-1) + 4\cdot n} = \frac{1}{n + 2\cdot (-1)}\cdot 2\cdot 4/4
|
5,932 |
z_1 = \operatorname{asin}(U) \Rightarrow U = \sin\left(z_1\right)
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8,456 |
(1 - 8*d)*(d + 1) * (d + 1) = 1 - 8*d^3 - 15*d * d - 6*d
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30,039 |
6 = \dfrac{1}{4^1\cdot 1!}\cdot 4!
|
15,924 |
-x \cdot 81 = -81 \cdot x + 0
|
-20,123 |
-14/(-8) = 7/4 (-2/(-2))
|
27,224 |
1 = (x\cdot y)^2 = x^2\cdot y^2\Longrightarrow x\cdot y = y\cdot x
|
1,678 |
(-x*2 + s)^2 = s^2 - s*x*4 + 4*x^2
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27,614 |
305*(1 + 0.5 + 0.5^2) = 305*(1 + 0.5)*0.5 + 305
|
762 |
0 = b^2 - 2*b*h + h^2 = \left(b - h\right)^2
|
17,521 |
1 = z^{18} \Rightarrow \left(z^{18}\right)^3 = z^{54} = 1
|
-15,257 |
\dfrac{r^2}{\frac{1}{\frac{1}{r^8} \cdot j^8}} = \frac{r^2}{\frac{1}{j^8} \cdot r^8}
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-5,736 |
\frac{3}{90\cdot (-1) + p^2 - p} = \frac{3}{(10\cdot (-1) + p)\cdot (p + 9)}
|
10,667 |
{k \choose p} = {k + (-1) \choose p} + {k + (-1) \choose (-1) + p}
|
33,841 |
0 = \left(-1\right) + 1 + (-1) + 1 + (-1) + 1
|
-10,495 |
-41/48 = -\frac{1}{48} \cdot 41
|
32,690 |
5 = \left\lceil{4.0929}\right\rceil
|
38,490 |
218 218 + (-1) = 219 \cdot 217 = 3 \cdot 73 \cdot 7 \cdot 31
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26,179 |
\frac{{7 \choose 0}}{{10 \choose 3}} \cdot {3 \choose 3} = 1/120
|
21,941 |
(m + 1)^2 - (m + (-1))^2 = m^2 + 2\times m + 1 - m^2 + 2\times m + (-1) = 4\times m
|
-5,105 |
0.79\cdot 10^0 = 0.79\cdot 10^{3 + 3(-1)}
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22,789 |
1 = \frac{\mathrm{d}y}{\mathrm{d}z}\cdot (z + y^2) \Rightarrow y^2 + z = \frac{\mathrm{d}z}{\mathrm{d}y}
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11,547 |
2\cdot \dfrac{1}{2}\cdot (\left(-1\right) + 2 - y) \cdot (\left(-1\right) + 2 - y) = (-y + 1)^2
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25,548 |
g h^2 g = \frac{1}{g h g} = h g h
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12,235 |
\frac{a^2*g^7}{g*a^3} = \frac{g^6}{a}
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-11,175 |
(z + 8(-1))^2 + c = (z + 8\left(-1\right)) \left(z + 8(-1)\right) + c = z^2 - 16 z + 64 + c
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13,281 |
\pi = 3 + (6 + \tfrac{3^2}{6 + \frac{1}{6 + \dotsm}\cdot 5^2})^{-1}
|
29,376 |
0 = x \Rightarrow \|x\| = 0
|
28,861 |
\left(g + b\right) \cdot (-b \cdot g + g^2 + b \cdot b) = g^3 + b^2 \cdot b
|
-23,108 |
-\tfrac74 = -1/2*\frac127
|
-21,609 |
\sin{-\pi \cdot 5/6} = -0.5
|
2,822 |
2\cdot (-3/2 + x) = x\cdot 2 + 3\cdot \left(-1\right)
|
20,420 |
\left\lfloor{\dfrac{1}{13} \cdot 200}\right\rfloor \cdot 3 + 4 = 49
|
24,077 |
1/36 + \dfrac19 + \frac{1}{9} = \frac{1}{4}
|
2,185 |
q + 5 \cdot q + 6 \cdot (-1) + 1 = 5 \cdot (-1) + 6 \cdot q
|
-9,729 |
-0.875 = -87.5/100 = -\frac18*7
|
13,197 |
e^{(E + B)\cdot t} = e^{E\cdot t}\cdot e^{B\cdot t} = e^{B\cdot t}\cdot e^{E\cdot t}
|
29,316 |
-p*x + r*n = -p*x + r*n - r*x + r*x
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-4,538 |
\frac{-y \cdot 6 + 3}{12 (-1) + y^2 - y} = -\frac{3}{y + 3} - \dfrac{1}{y + 4(-1)}3
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41,427 |
9604 = 98\cdot 98
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-18,275 |
\frac{1}{p^2 + \left(-1\right)}*(4*(-1) + p^2 + p*3) = \frac{1}{(1 + p)*((-1) + p)}*(p + 4)*(p + (-1))
|
3,605 |
\cos{z \times 2} = -2 \times \sin^2{z} + 1
|
7,225 |
\sin{\dfrac{2π}{5}} = -\sin{\frac{π*8}{5}}
|
2,045 |
BA T - ATB = 0 \implies BA T = 0
|
18,515 |
a^3 b^3 = \left(b a\right)^2 (a b)
|
29,024 |
(\sin^2(y))^{\dfrac{1}{2}} = |\sin(y)| = \sin(y)
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-20,540 |
5/5\cdot \frac{s}{3\cdot s + 2\cdot \left(-1\right)}\cdot 3 = \frac{1}{15\cdot s + 10\cdot \left(-1\right)}\cdot 15\cdot s
|
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