id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
24,796 |
1/\left(xR\right) = 1/(xR)
|
-3,266 |
3 \cdot 10^{1/2} = 10^{1/2} \cdot (1 + 2)
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29,686 |
\left(-(l - k)*2 + 4 = 0 \Rightarrow -k + l = 2\right) \Rightarrow k = 2(-1) + l
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22,534 |
\dfrac{1}{4 \cdot 3} = 1/12
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10,993 |
10^{18} \cdot 2.86 \cdot 0.9996 \cdot 0.972 \cdot 0.96^2 \cdot 0.95 = 20!
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18,866 |
\left(c + b\right)\cdot (-b + c) = -b^2 + c^2 \Rightarrow c + b = \left(c + b\right)\cdot \dfrac{c - b}{c - b} = \frac{c^2 - b^2}{c - b}
|
-20,023 |
(1 - g*8)/2*\frac{7}{7} = (-g*56 + 7)/14
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32,102 |
\dfrac{8*h^3}{h * h*2} = 4*h
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28,511 |
a^{y + x} = a^x \cdot a^y
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35,689 |
0 = -(111 + 11113 + 1111115) + 102030\cdot 11 + 9
|
-2,232 |
\frac{1}{19} \cdot 2 = 8/19 - 6/19
|
6,077 |
2 \cdot (-1) + z^4 = (\sqrt{2} + z^2) \cdot \left(z^2 - \sqrt{2}\right)
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-19,047 |
1/5 = \dfrac{A_s}{100 \cdot \pi} \cdot 100 \cdot \pi = A_s
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-18,084 |
2 = 15 + 13 (-1)
|
115 |
34/49 - \dfrac{18}{49} = \frac{1}{49} \cdot 16
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14,911 |
-\int_x^1 \dfrac{1}{q}\,\mathrm{d}q = \int_1^x \frac{1}{q}\,\mathrm{d}q
|
2,614 |
f \times g = \dfrac14 \times (-(f - g)^2 + (f + g)^2)
|
24,405 |
n! = (n + \left(-1\right))!*n
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23,044 |
x_5 x_3 = x_3 x_5
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-4,483 |
\dfrac{6 \cdot y + 17 \cdot (-1)}{6 + y^2 - 5 \cdot y} = \frac{5}{2 \cdot (-1) + y} + \dfrac{1}{y + 3 \cdot (-1)}
|
32,310 |
(-c \cdot h + f \cdot x)^2 + (x \cdot c + h \cdot f) \cdot (x \cdot c + h \cdot f) = (c^2 + f^2) \cdot (h \cdot h + x^2)
|
2,455 |
H \cdot I = H \cdot I
|
556 |
d^{b + \left(-1\right)} d = d^b
|
10,391 |
\frac{\sin{2*z}}{1 - \cos{2*z}} = \dfrac{2*\sin{z}*\cos{z}}{1 + (-1) + 2*\sin^2{z}} = \cot{z}
|
30,596 |
r \cdot (r + 1)/2 = 1 + 2 + 3 + \dots + r
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-5,091 |
1.83\cdot 10 = 1.83\cdot 10/10 = 1.83\cdot 10^0
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39,273 |
x = (1 + x_k)^k \geq k \cdot x_k
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-30,318 |
8-3= 5
|
1,130 |
\dfrac{1}{(3 \cdot (-1) + 84)! \cdot 3!} \cdot 84! = 95284
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-25,054 |
\dfrac{1}{14} \cdot 4 \cdot \frac{6}{13} = \frac{24}{182} = \frac{12}{91}
|
1,550 |
2/3 = \left(0 + 1 + 1\right)/3
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7,861 |
\lim_{x \to \infty} -M \cdot |g_x| = 0 = \lim_{x \to \infty} M \cdot |g_x|
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-8,336 |
20 = (-4)*(-5)
|
14,063 |
\mathbb{E}(X_t^2) \cdot \mathbb{E}(X_{t - j}^2) = \mathbb{E}(X_{t - j}^2 \cdot X_t^2)
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5,439 |
c^2 - 24 c + 144 = (c + 12 (-1))^2
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-17,067 |
-8 = -25*t^2 - 5*t - 8*(-5*t) - -8 = -25*t^2 - 5*t + 40*t + 8
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-4,554 |
x^2 - x\cdot 2 + 3\cdot (-1) = \left(1 + x\right)\cdot (3\cdot (-1) + x)
|
13,122 |
m - i = m - i - i*0
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-22,341 |
(j + 10) \times (j + 8 \times (-1)) = 80 \times (-1) + j^2 + 2 \times j
|
21,322 |
3 = -l\cdot 4 + 11\Longrightarrow l = 2
|
7,466 |
\sin(2\pi)+\sin(4\pi)=\sin(2\pi+4\pi)
|
3,453 |
\left(5\left(-1\right) + 2x = 0 \implies x*2 = 5\right) \implies x = 5/2
|
-5,257 |
10^{-1 + 2}\cdot 13.8 = 10^1\cdot 13.8
|
23,297 |
\frac{142}{n}\cdot x\cdot \pi = \pi \implies 142\cdot x = n
|
-17,786 |
6 = 53\cdot (-1) + 59
|
15,547 |
f_1\cdot F = f_2\cdot F \Rightarrow F/(f_1) = \frac{F}{f_2}
|
-20,828 |
\frac{1}{-s*14 + 56 (-1)}(24 (-1) - s*6) = \frac37 \frac{1}{8(-1) - s*2}(-2s + 8(-1))
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38,797 |
100\cdot \left(-1\right) + 100\cdot 2 + 100\cdot 3 + 100\cdot (-4) + 100\cdot 5 + 100\cdot \left(-6\right) = -100
|
5,313 |
7/6 = 1/2 + \dfrac{1}{3} + \frac13
|
7,396 |
(h + 0*\left(-1\right))*(h + 0*(-1)) = \left(h + 0\right)*(h + 0*\left(-1\right)) = h
|
11,583 |
(1 + i)\cdot (i + 2)\cdot (2\cdot i + 3)/6 = \dfrac{1}{6}\cdot (i + 1)\cdot (1 + 2\cdot (i + 1))\cdot (i + 1 + 1)
|
13,274 |
\tfrac{1}{2^2} = \tfrac{2^0}{2^2} = \dfrac{1}{4}
|
21,600 |
(a + c)^{p + (-1)}\cdot (a + c) = (c + a)^p
|
383 |
0 = E(X^5) rightarrow E(X \cdot X \cdot X) = 0
|
51,799 |
36=2\times 18=6\times 6
|
41,684 |
\frac{4}{36} = 1/9
|
14,285 |
\frac12 = \frac{1}{12}\cdot 6
|
-10,784 |
\frac15 \cdot 5 \cdot \frac{1}{16 \cdot x^3} \cdot 8 = \frac{40}{80 \cdot x^3}
|
-7,790 |
\frac{1}{32}(48 + 48 i + 48 i + 48 \left(-1\right)) = (0 + 96 i)/32 = 3i
|
35,683 |
\alpha*\beta*z = z*\beta*\alpha
|
21,693 |
V = V \cap F(f*b) = (V \cap F(b)) \cup \left(V \cap F(f)\right)
|
-15,924 |
-\frac{44}{10} = 10/10 - 6*9/10
|
3,646 |
(a + (-1)) \cdot \left(1 + a\right) = (-1) + a^2
|
-14,564 |
7 + 10 \times 3 = 7 + 30 = 37
|
17,640 |
m^2 = \left(100*c*m\right)^2 = 10000*c*m^2
|
-1,589 |
-\frac{1}{4}\pi + 2 \pi = \frac{7}{4}\pi
|
21,296 |
|-h*d + d_k*h_k| = |d_k*h_k - d*h + h*d_k - h*d_k|
|
5,112 |
2\cdot n + 1 = (n + 1)\cdot 2 + (-1)
|
27,210 |
y^2 - 2 y + 3 (-1) = (3 (-1) + y) (y + 1)
|
37,491 |
\sin(y) = \frac{1}{\sec(y)} \cdot \tan(y)
|
8,864 |
e^{\tfrac{1}{1 + \left(-1\right)}} = e^{-1/0} = e^{-∞} = 0
|
377 |
\dfrac{29*24*30}{5*3*2} = 696
|
25,748 |
\mathbb{E}\left[Q_1*Q_2\right] = \mathbb{E}\left[Q_2\right]*\mathbb{E}\left[Q_1\right]
|
9,986 |
(-1) + 5^k \cdot (6 + \left(-1\right)) = 6 \cdot 5^k + 6 \cdot (-1) - 5^k + 5
|
11,701 |
3^{z + (-1)} = 2 + 1 \Rightarrow z = 2
|
33,849 |
\frac{10 \cdot x}{10 \cdot x + 3} \cdot 1 = \frac{1}{10 \cdot x + 3} \cdot (10 \cdot x + 3 + 3 \cdot (-1)) = 1 - \frac{3}{10 \cdot x + 3}
|
-1,769 |
13/12\cdot \pi + 3/4\cdot \pi = \frac{11}{6}\cdot \pi
|
-10,861 |
31 = \frac{1}{6} 186
|
35,701 |
(\frac{m!^m}{m^{4 \cdot m}})^{\frac1m} = \frac{m!}{m^4} \approx \frac{1}{m^4}
|
3,611 |
h_{i\cdot i} = -h_{i\cdot i} \Rightarrow 0 = h_{i\cdot i}
|
8,012 |
2*\left(y^4 + y^2\right) - y^4*2 = 2*y^2
|
-27,483 |
3*x*x*5*3 = 45*x^2
|
17,834 |
\sum_{n=-\infty}^\infty \frac{1}{n^p} = \sum_{n=1}^\infty \frac{1}{n^p} + \sum_{n=-\infty}^1 \dfrac{1}{n^p} = 2*\sum_{n=1}^\infty \frac{1}{n^p}
|
-19,467 |
\frac{\tfrac{1}{2} \cdot 3}{\tfrac{1}{3} \cdot 8} = 3/8 \cdot 3/2
|
26,893 |
x=-\frac12\times-2x
|
-28,199 |
d/dz (-3 \cdot \cot{z}) = -3 \cdot d/dz \cot{z} = 3 \cdot \csc^2{z}
|
30,534 |
i = 2^{2 (x + 1)} + \left(-1\right) = 4*4^x + (-1)
|
36,499 |
c_A = c_A
|
5,856 |
\left(-2\right)\times (-1) + x = x + 2
|
-22,273 |
(10 + x)\cdot (1 + x) = x^2 + x\cdot 11 + 10
|
41,721 |
\binom{7}{3}*4! = \dfrac{1}{3!*4!}*7!*4! = \frac{1}{3!}*7!
|
1,693 |
2 \cdot \left(1/2 \cdot 147 \cdot 2 + \frac12 \cdot 74 \cdot 3 + 1/2 \cdot 146 \cdot 2\right) = 808
|
5,461 |
\frac{3}{21} = \frac{6}{42}
|
17,346 |
1/w u/1 = \dfrac{u}{w}
|
10,421 |
g x g = g = g x g
|
-29,810 |
x * x*3 = d/dx x * x * x
|
2,858 |
0 = 1/h + 1/b + \frac{1}{c} \Rightarrow (hc + hb + bc)/(hbc) = 0
|
34,399 |
2499 = 51\cdot 49
|
-27,710 |
12 \cdot \sin{y} = \frac{\mathrm{d}}{\mathrm{d}y} (-12 \cdot \cos{y})
|
21,588 |
(x + 1)^4*(x + 1) = (x^4 + 1)*(x + 1) = x^5 + x^4 + x + 1
|
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