id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-260 |
\frac{8!}{(8 + 6(-1))!*6!} = \binom{8}{6}
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-3,865 |
\tfrac{\dfrac{1}{2}*3}{x * x * x} = \frac{3}{2*x^3}
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-28,641 |
6 \cdot x \cdot x + 36 \cdot x + 78 = 6 \cdot (x \cdot x + 6 \cdot x + 13) = 6 \cdot (x \cdot x + 6 \cdot x + 9 + 4) = 6 \cdot ((x + 3)^2 + 4) = 6 \cdot ((x + 3)^2 + 2^2)
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15,739 |
-3 \cdot \left(2^{20} + (-1)\right) + 3^{20} = 3 \cdot (1 + 3^{19} - 2^{20})
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26,745 |
\left(2*k\right)^2 = 2*(m*2)^2 \implies k * k = 2*m^2
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29,722 |
f*y*z = y*z = y*z = f*y*z
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8,348 |
(a + 1) (d + 1) + (-1) = a + d + ad
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5,170 |
\frac{a^3 - b^3}{a^2 + a \cdot b + b^2} = -b + a
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6,275 |
1/30 = \frac{1}{3}\cdot \frac{1}{10}
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-19,623 |
1/(5/9\times 6) = 9\times 1/5/6
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42,416 |
\frac{1}{30} \cdot 10 = 1/3
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-5,617 |
\frac{5}{4\times \left(8 + t\right)} = \frac{5}{32 + t\times 4}
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8,689 |
1 + y^{1/3} = 0 rightarrow y^{1/3} = -1
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29,070 |
C_2*B*C_1 = B*C_1*C_2
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3,635 |
y^2 - 4 \times y + 12 \times (-1) = (y + 6 \times (-1)) \times (2 + y)
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38,279 |
56 = 2 2*14
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42,509 |
2 2 \cdot 0.01 + 0.02 = 0.06
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-10,450 |
-4 = -5 + j + 1 = j + 4\cdot \left(-1\right)
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4,936 |
(-1) + \mathbb{E}[T] = \mathbb{E}[(-1) + T]
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14,106 |
80 = \tfrac13\cdot 2\cdot 120
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5,851 |
e^{(\left(-1\right) \cdot x)/2} \cdot e^{\frac12 \cdot \left(x \cdot \left(-1\right)\right)} = e^{-x}
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2,820 |
m\cdot 8 = m\cdot (3 + 5)
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33,222 |
(-f + h)^2 = f^2 + h^2 - 2\cdot h\cdot f
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-27,661 |
\tfrac12 7 = \dfrac{7}{2}
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11,427 |
V \cdot Y + V \cdot W = V \cdot (W + Y)
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8,301 |
0 = z^3 - 2z^2 - 5z + 6 = (z + (-1)) (z + 2) \left(z + 3\left(-1\right)\right)
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-11,912 |
0.01601 = 1.601 \cdot 0.01
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30,947 |
6^x = (3 \cdot 2)^x = 3^x \cdot 2^x = 2^x + 2^x \cdots \cdots
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6,227 |
\sec(\theta) := \frac{1}{\cos\left(\theta\right)}
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17,188 |
n + 2(-1) = n + 4(-1) + 2
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33,872 |
1 + x \cdot x + \left(-1\right) = x^2
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7,991 |
p = -\dfrac{1}{2 \cdot q} \cdot \left(\left(-2\right) \cdot q \cdot p\right) = -\frac{1}{2 \cdot q} \cdot ((-1) \cdot q \cdot p^2)
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-19,587 |
\dfrac{7*\frac{1}{4}}{1/5*9} = 5/9*\dfrac{7}{4}
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24,314 |
\left(-b + x\right) \left(x + b\right) = x x - b^2
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18,431 |
\left(6\cdot l_1 + 3\cdot (2\cdot l_2 + 1) = 9 = 6\cdot \left(l_1 + l_2\right) + 3 \implies 1 = l_1 + l_2\right) \implies 1 - l_2 = l_1
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-23,246 |
2/9 = \frac42\frac{1}{9}
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30,636 |
36 = 3! \cdot 2! \cdot 3
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6,866 |
\dfrac{x^2 + x}{(-1) \cdot x} = (-1) - x
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8,146 |
\frac{1}{(1 - w \cdot w) \cdot (1 - w \cdot w)} = \frac{1}{((w + (-1)) (w + 1)) \cdot ((w + (-1)) (w + 1))} = \frac{1}{(w + (-1))^2 (w + 1) \cdot (w + 1)}
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75 |
1/33 + \frac{1}{11} + \frac{1}{22} = 1/6
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19,756 |
0\cdot ( 1, 4, 0) + ( 2, 2, 2)\cdot 0 = 0
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-1,860 |
\pi\cdot \frac{11}{6} - \frac16\cdot \pi = \pi\cdot 5/3
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-22,290 |
21 + y^2 - y\cdot 10 = (y + 3\cdot \left(-1\right))\cdot (y + 7\cdot (-1))
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-20,030 |
\frac{1}{5x + 2}\left(x \cdot 5 + 2\right) \tfrac{1}{7}4 = \frac{1}{14 + 35 x}\left(8 + x \cdot 20\right)
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12,553 |
E\left[N\right] E\left[X\right] = E\left[NX\right]
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-14,125 |
\frac{1}{10 + 9(-1)}2 = \frac112 = \frac{2}{1} = 2
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-20,407 |
\frac{1}{4} \cdot 4 \cdot \frac{3 - p \cdot 10}{(-1) \cdot 6 \cdot p} = \frac{12 - p \cdot 40}{(-24) \cdot p}
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22,829 |
8/2 = \tfrac{1}{2}*2 + \frac{6}{2}
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11,106 |
5! \cdot {26 \choose 3} \cdot {10 \choose 2} = 14040000
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13,650 |
a^2 + b^2 = \dotsm = a \times a\times b \times b
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-6,139 |
\frac{3 \cdot a}{12 \cdot (-1) + a^2 + a} = \dfrac{a \cdot 3}{(4 + a) \cdot (3 \cdot (-1) + a)}
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4,013 |
b*h + h + b + 1 = (b + 1)*(1 + h)
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27,118 |
\frac{\mathrm{d}z}{\mathrm{d}x} = \frac{1}{z^2} + 4\cdot (-1) = \frac{1}{z^2}\cdot (1 - 4\cdot z^2)
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25,511 |
(36 + 1)^{1 / 2} = 6*(1 + \frac{1}{36})^{\frac{1}{2}} = 1 + 1/72 - \dots
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-534 |
({ e^{23\pi i / 12}}) ^ {2} = e ^ {2 \cdot (23\pi i / 12)}
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34,026 |
(R + 1)! = R!\cdot (R + 1)
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-6,388 |
\frac{20}{4 \cdot (4 \cdot (-1) + q) \cdot (q + 6)} = 4/4 \cdot \frac{5}{\left(q + 6\right) \cdot \left(4 \cdot (-1) + q\right)}
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-22,440 |
16^{-\dfrac{5}{4}} = (\frac{1}{16})^{\frac{1}{4}\cdot 5} = (\left(\frac{1}{16}\right)^{\frac{1}{4}})^5
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-30,266 |
(y + 3)\cdot (y + 2\cdot (-1)) = 6\cdot (-1) + y^2 + y
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28,070 |
25/36 = 2*5/6*5/6/2
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38,495 |
x * y = y * x
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49,105 |
495 = 5\times 9\times 11
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22,305 |
q \cdot 6 = 0 rightarrow q = 0
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23,790 |
1/3\cdot 4 = 4/3
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15,155 |
\frac13*2 = \dfrac{2}{2 + 3 + 2*(-1)}
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21,556 |
1/2 + ((-1) + m)/4 = (1 + m)/4
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-6,667 |
\frac{5}{x*3 + 12 (-1)} = \frac{5}{(x + 4(-1))*3}
|
941 |
exp(y + B) = exp(B)\cdot exp(y)
|
3,125 |
\cos{\frac{1}{6} \cdot \pi \cdot 7} = \cos{\frac16 \cdot ((-1) \cdot 7 \cdot \pi)}
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-3,536 |
\frac{1}{100} \cdot 35 = \frac{7 \cdot 5}{5 \cdot 20}
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12,648 |
(n - k)!\cdot \binom{n}{k} = n!/k!
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30,970 |
x = 2x/4\cdot 2
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9,094 |
\left(A + y\cdot I\right)\cdot (x\cdot I + A) = (I\cdot y + A)\cdot (x\cdot I + A)
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-18,571 |
3 \cdot z + 2 \cdot (-1) = 9 \cdot \left(2 \cdot z + 1\right) = 18 \cdot z + 9
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32,128 |
S\cdot \beta = \beta\cdot S
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24,320 |
E_s + E_s = E_s*2
|
568 |
fg = (-g^2 + (g + f)^2 - f^2)/2
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18,803 |
1 = 1^{-1}*\frac{1}{1}/1
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36,361 |
|5403 + 5403 \times \left(-1\right)| = 0
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30,542 |
(5^{\frac{1}{2}})^2 - 2*5^{\frac{1}{2}} + 1 = (5^{1 / 2} + \left(-1\right))^2
|
30,107 |
32 + y^{15} \cdot 31 - y^{10} = 0 \implies 0 = \left(y^{15} + 1\right) \cdot 31 - \left(-1\right) + y^{10}
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-11,564 |
-7i - 6 + 3\left(-1\right) = -9 - 7i
|
5,511 |
h' \times k' \times f \times l = f \times l \times k' \times h'
|
6,980 |
\frac{1}{d^{\frac12} g^{-3/2}} = \frac{g^{3/2}}{d^{\frac12}}
|
-3,927 |
110/10 \dfrac{m^5}{m^4} = \frac{110 m^5}{10 m^4}
|
25,434 |
-\frac{x}{2} + \frac{3}{x} = -x/2 + \frac3x
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11,596 |
5^5 - 4 \cdot 5^4 + 6 \cdot 5^3 - 5 \cdot 5 \cdot 4 + 5 = 1280
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5,576 |
3/6\cdot 4/10\cdot \frac23 = \frac{1}{15}\cdot 2
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-5,394 |
10^6*59.4 = 10^{1 + 5}*59.4
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22,570 |
f = b\Longrightarrow \left\{f,b\right\}
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-26,502 |
9 + 25 x^2 - 30 x = 3^2 + (x\cdot 5)^2 - x\cdot 5\cdot 3\cdot 2
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36,277 |
x^2 + 2 \cdot x \cdot y + y^2 = (x + y) \cdot (x + y)
|
20,858 |
X\frac{\mathrm{d}Y}{\mathrm{d}X} + Y = \frac{\partial}{\partial X} \left(YX\right)
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28,365 |
(d - f) \cdot (d - f) = (d - f) \cdot \left(d - f\right) = d^2 - 2 \cdot d \cdot f + f^2
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18,135 |
(z^2 + z\cdot 20 + 180)\cdot (18\cdot (-1) + z^2 - z\cdot 2) = z^4 + 18\cdot z^3 + z^2\cdot 122 - 720\cdot z + 3240\cdot (-1)
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-2,245 |
-\frac{1}{11} + 5/11 = \dfrac{4}{11}
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12,847 |
\frac{\frac{1}{6}}{6}*5/6 = \dfrac{5}{216} = 0.023
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43,865 |
9 = 12 + 3 \cdot (-1)
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6,140 |
1.73205081\cdot \dotsm/3 = \sqrt{3}/3
|
9,619 |
\sin\left(x + z\right) = \sin(x)*\cos\left(z\right) + \sin(z)*\cos(x) = \sin(x) + \sin\left(z\right)
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