id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
2,655 |
(a + x)^4 - 4a^3 x - a^2 x^2*6 - ax^3*4 = a^4 + x^4
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-4,080 |
32\cdot x \cdot x/(x\cdot 48) = \frac{32}{48}\cdot \frac1x\cdot x^2
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47,049 |
30 \times 4 = 120 = 1 + 17 \times 7
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9,048 |
\left( 5, 9, 0\right) = ( 2, 1, -5) + ( x, y, z)\Longrightarrow ( 5, 9, 0) = ( 2 + x, y + 1, 5 \cdot (-1) + z)
|
11,071 |
(4^6)^{96} \cdot 4^2 = 4^{578}
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-3,821 |
2h^4 = 2h^4
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4,976 |
\left(10 + x\right)*x = x^2 + 10*x
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8,996 |
0 < \left(-1\right) + f rightarrow 1 < f
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20,163 |
0\times 0 - \frac{1}{2}\times 1/2 = -1/4 \lt 0
|
-25,237 |
z \cdot 5/2 = \frac{\mathrm{d}}{\mathrm{d}z} \sqrt{z^5}
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21,380 |
|\frac{x + \left(-1\right)}{x + 1} + (-1)| = |-\frac{2}{x + 1}| = \dfrac{2}{|x + 1|}
|
-1,756 |
\pi + \pi\cdot \frac{1}{12}\cdot 5 = \pi\cdot \frac{17}{12}
|
25,048 |
det\left(H \cdot Z\right) = det\left(H\right) \cdot det\left(Z\right) = det\left(Z\right) \cdot det\left(H\right) = det\left(Z \cdot H\right)
|
10,662 |
\dfrac{n}{\binom{2\cdot n}{2}} = \dfrac{1}{2\cdot n\cdot (2\cdot n + (-1))\cdot 1/2}\cdot n = \frac{1}{2\cdot n + \left(-1\right)}
|
7,507 |
2/9 \cdot t_{2 \cdot (-1) + m} = \frac{1}{3} \cdot 2 \cdot \frac{1}{3} \cdot t_{2 \cdot (-1) + m}
|
39,013 |
\cos(π - x) = -\cos(x)
|
29,566 |
128 = -16 \approx Y \Rightarrow -8 = Y
|
-1,686 |
2\cdot \pi - \frac54\cdot \pi = \frac{3}{4}\cdot \pi
|
-1,178 |
45/72 = \frac{5}{72 \cdot 1/9} \cdot 1 = \frac58
|
-10,740 |
\frac{1}{k + 3}\cdot \left(k\cdot 2 + 9\cdot (-1)\right)\cdot \frac44 = \frac{8\cdot k + 36\cdot (-1)}{k\cdot 4 + 12}
|
28,032 |
|\lambda x| = |x| |\lambda|
|
809 |
z! = 10!*11*12 \dots z \gt 10!*11^{z + 10 \left(-1\right)}
|
36,078 |
\dotsm = 1 - 1 + 1 - 1 + 1 - 1 + \dotsm
|
14,720 |
w = \frac{z}{x} \Rightarrow z = w \cdot x
|
26,141 |
\cos^2 \theta= 1-\sin^2\theta
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26,596 |
\left((-1) + z\right) \cdot \left(2 \cdot \left(-1\right) + z\right) = 2 + z^2 - z \cdot 3
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46,730 |
\int_1^x \frac{1}{1 + t^2}\,\mathrm{d}t = \int_{\frac1x}^1 \frac{\frac{1}{t^2}}{1 + (1/t)^2}\cdot 1\,\mathrm{d}t = \int\limits_{1/x}^1 \frac{1}{1 + t \cdot t}\,\mathrm{d}t
|
18,555 |
\mathbb{E}(X + Q) = \mathbb{E}(Q) + \mathbb{E}(X)
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31,154 |
4! \cdot 13 \cdot 11 \cdot 10 \cdot 36 \cdot 12 = 14826240
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2,716 |
A\cdot h = A\cdot h
|
17,984 |
\frac{1}{324}144 = 4/9
|
22,091 |
3\times 2 + 2^3 = 14
|
-1,964 |
19/12 \pi + \frac76 \pi = \dfrac{11}{4} \pi
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31,802 |
\frac{1 + \sqrt{6}}{12} = \frac{1}{12} + \frac{\sqrt{6}}{12}
|
-10,710 |
20 = -40\times y + 140 + 5\times (-1) = -40\times y + 135
|
5,422 |
z\cdot (z + \left(-1\right)) = -z + z^2
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28,252 |
\cos(2(x + (-1))) = \cos(2x + 2(-1))
|
9,829 |
\sin{y} = \cos{y} \implies \tan{y} = 1
|
356 |
\frac{1}{5}\cdot 0 + 4\cdot 1/5/3 = 4/15
|
4,244 |
\left|{AA^W}\right| = 0 = \left|{A^W A}\right|
|
6,200 |
(x^2 + 1)\cdot 0 + 5\cdot 3 + 12 (\left(-1\right) + x) = 3 + x\cdot 12
|
2,301 |
(8k)^2/2=32k^2
|
-10,438 |
\frac{\eta\cdot 5 + (-1)}{6\cdot (-1) + \eta\cdot 2}\cdot 3/3 = \frac{15\cdot \eta + 3\cdot (-1)}{6\cdot \eta + 18\cdot (-1)}
|
22,038 |
1/(\sqrt{y}) = y^{-\frac{1}{2}}
|
340 |
\dfrac{1}{B + (-1)}*(B^9 + \left(-1\right)) = 1 + B + \dots + B^8 = \mathbb{P}(B)
|
-30,918 |
12\times y + 15\times (-1) = y\times 12 + 15\times (-1)
|
10,667 |
{(-1) + m \choose p + (-1)} + {m + (-1) \choose p} = {m \choose p}
|
25,230 |
(-2 + 1)^2 + (0 + 1)^2 - 0 \cdot (-2 + 0 + 3) \cdot 2 = 2
|
9,524 |
-\frac{1}{y + (-1)} = \frac{1}{1 - y}
|
2,869 |
|A| = B \Rightarrow A^2 = |A| |A| = BB = B \cdot B
|
7,041 |
1 - \frac{6!\cdot 2!}{7!}\cdot 1 = 5/7
|
-13,825 |
\frac{5}{9 + 8 \cdot \left(-1\right)} = \frac{1}{1} \cdot 5 = 5/1 = 5
|
-3,198 |
\sqrt{6} \cdot \sqrt{4} + \sqrt{25} \cdot \sqrt{6} = 2 \cdot \sqrt{6} + \sqrt{6} \cdot 5
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-2,269 |
\dfrac{9}{12} = -1/12 + 10/12
|
4,390 |
\left(m + (-1)\right) ((-1) + m)! = -(m + (-1))! + m!
|
19,821 |
\left(\frac{4}{120} + \tfrac{1}{4} + 1/6 + \tfrac12\right) \times 8! = 38304
|
-22,198 |
h \cdot h - 4 \cdot h + 3 = (h + 3 \cdot (-1)) \cdot ((-1) + h)
|
-16,941 |
-3 = -3*\left(-5*n\right) - -18 = 15*n + 18 = 15*n + 18
|
30,495 |
\frac{\mathrm{d}}{\mathrm{d}x} x \cdot x = 2\cdot x
|
27,138 |
\frac{1}{5} = \frac{1}{30} + \frac{1}{24} + 1/8
|
21,761 |
(h^2 + b \cdot b) \cdot (c^2 + d^2) = (h \cdot c + b \cdot d) \cdot (h \cdot c + b \cdot d) + \left(h \cdot d - b \cdot c\right)^2 = \left(h \cdot c - b \cdot d\right)^2 + (h \cdot d + b \cdot c)^2
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-10,530 |
-\frac{40 \cdot (-1) + y \cdot 4}{20 + 4 \cdot y} = -\frac{1}{5 + y} \cdot (y + 10 \cdot (-1)) \cdot 4/4
|
10,420 |
\left(5^n + \left(-1\right)\right) \left(1 + 5^n\right) = (-1) + 5^{n\cdot 2}
|
11,322 |
m + 2 \cdot \binom{m}{2} = m^2
|
-18,591 |
5 e + 9 (-1) = 10*(5 e + 5 \left(-1\right)) = 50 e + 50 (-1)
|
12,255 |
7 = |11 + 4\times (-1)|
|
15,956 |
\sin(2 \cdot y) = \tfrac{2 \cdot \tan(y)}{\tan^2(y) + 1} \cdot 1
|
12,269 |
d \cdot n_i + (1 + n_i) \cdot b = L_i rightarrow \frac{L_i - b}{d + b} = n_i
|
1,509 |
(z*\left(-1\right))/\left(-2\right) = (z*(-1))/(\left(-1\right)*2)
|
383 |
0 = E[A^5] \Rightarrow E[A^3] = 0
|
-1,895 |
0 + \pi\cdot \frac{7}{12} = \frac{7}{12}\cdot \pi
|
30,022 |
\frac{\frac{1}{2}}{x + \left(-1\right)} + \frac{1/2\cdot \left(-1\right)}{x + 1} = \frac{1}{(1 + x)\cdot (x + (-1))}
|
-20,828 |
3/7*\frac{8*\left(-1\right) - q*2}{-q*2 + 8*(-1)} = \dfrac{1}{56*(-1) - 14*q}*(24*(-1) - 6*q)
|
29,673 |
2\cdot k + (2\cdot k + 1)^3 + 1 = 8\cdot k^3 + 12\cdot k^2 + 8\cdot k + 1 = 4\cdot (2\cdot k^3 + 3\cdot k^2 + 2\cdot k + 1)
|
9,588 |
H \cap x = H rightarrow \{H, x\}
|
12,188 |
n*2 - k*2 \geq 1 + n rightarrow k \leq \left((-1) + n\right)/2
|
-17,388 |
\dfrac{113.6}{100} = 1.136
|
24,598 |
z^2 + z + 1 - 1 + 2\cdot z = z^2 - z
|
14,797 |
z^2 - 2\cdot z + 5 = z^2 - 2\cdot z + 1 + 4 = \left(z + (-1)\right)^2 + 4
|
27,980 |
2^{n + 1} + 2^{n + 1} = 2*2^{1 + n}
|
698 |
\dfrac{1}{3} \cdot 0 + 2/3 \cdot (1/2 + 1/2) = 2/3
|
-8,305 |
(-8)\cdot (-6) = 48
|
25,015 |
-1 = \left(1 + 3(-1) + 1\right)^{111}
|
2,596 |
(-3)^{\dfrac{1}{2}} \cdot (-2)^{\dfrac{1}{2}} = -(3 \cdot 2)^{\frac{1}{2}} = -6^{1 / 2} = -2.449
|
29,260 |
\binom{N + (-1)}{m + (-1)} = \binom{N - m + m + (-1)}{(-1) + m}
|
14,079 |
(a^2 + b^2) \cdot (a^2 + b^2) = \left(2 \cdot a \cdot b\right)^2 + (-b^2 + a^2)^2
|
-11,483 |
i\cdot 30 + 20 = 30\cdot i - 5 + 25
|
323 |
(i\cdot 16)^{-1} = (4i)^{-1} - 3/(i\cdot 16)
|
10,289 |
i\times \sin\left(\frac12\times π\right) + \cos\left(\frac{π}{2}\right) = i
|
6,131 |
\cos{z} = \cos\left(\tfrac{1}{4}\cdot \pi + z - \frac{\pi}{4}\right)
|
5,387 |
\frac{39}{212} + 2 = 463/212
|
38,634 |
U \times \pi/\pi = U
|
8,025 |
D = D \cap X \implies \{D, X\}
|
870 |
5^4 = \left(3^2 + 4 \times 4\right) \times 5^2
|
32,371 |
b \cdot a + a \cdot c + c \cdot b = ((a + b + c)^2 - a^2 + b \cdot b + c^2)/2
|
17,463 |
z^{7/3} = z^{4/3 + \dfrac133} = z^{4/3} z^{3/3} = z^{4/3} z
|
-10,394 |
-\frac{z + 8}{4 \cdot z + 2} \cdot \frac14 \cdot 4 = -\dfrac{1}{z \cdot 16 + 8} \cdot (32 + 4 \cdot z)
|
14,966 |
\sin{\beta} \cos{\beta}*2 = \sin{2 \beta}
|
21,052 |
30/5 + \left(-1\right) = 6 + (-1) = 5
|
-11,953 |
\frac{2}{5} = s/\left(20*\pi\right)*20*\pi = s
|
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