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ddrg
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math_formulas

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int64
-30,985
55.9k
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20,915
x_k\cdot X_k = x_k\cdot X_k
35,210
-x + k = 1 \Rightarrow k + \left(-1\right) = x
9,455
B \cdot A = I \implies A \cdot B = I
2,162
150 - 3/2\cdot x = \left(600 - 6\cdot x\right)/4
4,587
5 \cdot \dfrac{1}{216}/\left(1/12\right) = 5/18
5,759
v \cdot v^T \cdot W = v \cdot W \cdot v^T
4,407
99*(99 + 1) (198 + 1 + 1) = 200*100*99
31,876
x^2 + 8 \cdot x + 7 = (1 + x) \cdot (x + 7)
-2,530
6\cdot 6^{1/2} = 6^{1/2}\cdot (4 + 2)
30,053
l \cdot \binom{m}{l} = (m - l + 1) \cdot \binom{m}{l + (-1)} = m \cdot \binom{m + \left(-1\right)}{l + (-1)}
28,682
\lim_{z \to \infty} \sin{z} = \lim_{z \to 0^+} \sin{\frac1z}
-22,213
18 + x^2 - 11*x = (x + 2*(-1))*(9*\left(-1\right) + x)
25,844
0 = v*2 \implies v = 0
14,533
1/24 = \frac{1/6}{4}
19,604
x*u + u*n = u*\left(x + n\right)
-6,728
\tfrac{2}{100} + \frac{8}{10} = \frac{2}{100} + 80/100
19,766
det\left(A \cdot A^T\right) = det\left(A^T \cdot A\right)
25,243
\frac12\cdot2\pi=\pi
31,104
1328/2450 = 1 - \frac{34}{50} \cdot \dfrac{1}{49} \cdot 33
11,885
\cos(\frac{\pi}{8}) = \frac{1}{2} \cdot \sqrt{\sqrt{2} + 2}
19,759
x_n\sqrt{n}=\frac{x_n}{\frac{1}{\sqrt{n}}}
18,061
\dfrac{1}{36} + \tfrac{1}{18} + \frac{1}{12} = (1 + 2 + 3)/36 = 6/36 = 1/6
7,129
\sqrt{S_n} = x_n \Rightarrow S_n = x_n^2
2,390
\frac{1}{-\sin{x}\cdot 4 + \cos{x}}4 = r \implies -4\sin{x} r + r\cos{x} = 4
14,661
x = \sin^2(p) \implies \cos(2\cdot p) = 1 - 2\cdot \sin^2(p) = 1 - 2\cdot x
25,044
\dfrac{1}{-x + x^2} + \frac{x^2}{-x + x^2} = \frac{1}{-x + x^2}\cdot (1 + x^2)
22,644
U \cdot |U|^{2 \cdot (-1) + p} = u \Rightarrow u \cdot |u|^{\frac{1}{p + (-1)} \cdot (2 - p)} = U
22,998
{7 \choose 2}\cdot {10 \choose 1}\cdot 3\cdot 2 = 1260
7,868
y = \frac{1}{e}*y*e
6,703
C^k*C = C^{k + 1}
-9,265
-35 d^2 + d\cdot 14 = -5\cdot 7 d d + 2\cdot 7 d
-22,193
(9 \cdot \left(-1\right) + q) \cdot \left(6 + q\right) = 54 \cdot (-1) + q^2 - 3 \cdot q
-3,257
(3 + 2 \cdot (-1)) \cdot 2^{1/2} = 2^{1/2}
13,008
4960 = 10^4 - 10\cdot 9\cdot 8\cdot 7
29,480
112 = 9\left(-1\right) + 121
-1,334
7/3 (-\frac19) = \frac{1}{3 \cdot 1/7} ((-1) \dfrac19)
-18,250
\tfrac{1}{z^2 - z\cdot 7}\cdot (z \cdot z - 6\cdot z + 7\cdot \left(-1\right)) = \frac{\left(z + 1\right)\cdot (7\cdot (-1) + z)}{z\cdot \left(z + 7\cdot (-1)\right)}
-10,600
5/5 \cdot \frac{10}{y + 3 \cdot (-1)} = \frac{50}{5 \cdot y + 15 \cdot \left(-1\right)}
-16,612
5 \cdot 4^{\tfrac{1}{2}} \cdot 2^{1 / 2} = 5 \cdot 2 \cdot 2^{1 / 2} = 10 \cdot 2^{1 / 2}
-19,408
8/5\cdot 6/1 = \frac{6}{5}\cdot 8 = \frac{48}{5}
-10,513
-\dfrac{8}{5 + 2 \cdot t} \cdot 3/3 = -\frac{1}{t \cdot 6 + 15} \cdot 24
3,081
(2 + k^2 + 3*k)*(k + 1) = \left(1 + k\right)^2*(k + 2)
14,991
a \cdot c < a^2 + c \cdot c - a \cdot c \Rightarrow a^3 + c^3 \gt a \cdot c \cdot (a + c) = a^2 \cdot c + a \cdot c^2
27,728
b*a*a*b = a*a*b*b
32,389
1729 = 1^3 + 12^3
1,744
1 + x^2 + x = \frac14*3 + (x + \frac12)^2
29,723
1/45057474 = \frac{1}{\frac{1}{6! \cdot 53!} \cdot 59!}
3,911
(y + 1)^3 = y \cdot y^2 + y^2 \cdot 3 + y \cdot 3 + 1
5,606
\left(1 + y\right)^{m*2} = (1 + y)^m*\left(y + 1\right)^m
11,061
0 = a^2 + h^2 - a \cdot h \cdot 2 \Rightarrow (a - h)^2 = 0
8,820
g*e*f = e*f*g
23,993
(x + h)*(x + U) = x^2 + h*x + U*x + h*U = x^2 + (h + U)*x + h*U
11,054
(2 + i)^2 = 4 + i^2 + 4i
-8,091
\dfrac{-23 - 15 i}{-5 - i} = \dfrac{1}{-5 - i}(-23 - 15 i) \frac{1}{-5 + i}(i - 5)
37,979
3^{20\cdot j} = 9^{10\cdot j}
7,028
x^2/49 = y^2/1 = z^2/9 = \frac{1}{9}(x + y - z)^2
8,694
(z^{2^j})^2 = z^{2^{j + 1}}
20,175
\dfrac{4 / 27}{2}1 = \tfrac{4}{54}
44,406
1 = 2*5 + 9(-1)
31,057
g\cdot \frac{a\cdot b}{f} = \frac{b}{f}\cdot a\cdot g
628
\sum_{l=1}^x \left(x + 1 - l\right) = \sum_{l=1}^x x + \sum_{l=1}^x 1 - \sum_{l=1}^x l
35,809
499 = \dfrac{124750}{250}
-8,829
168 = 7*6*4
1,868
\frac{f}{b\cdot g} = f/(b\cdot g)
21,051
\frac{dt}{dq} = \frac{4 \cdot t^2}{4 \cdot t \cdot q} = t/q
18,622
\left(x^4 + z^4\right)^2 = \left(x^4 - z^4\right)^2 + (2 \cdot x^2 \cdot z^2)^2
7,639
(1 - 3k)^2 - 4k^2 = 1 - 6k + 5k * k = 5\left(k - 1/5\right) (k + (-1))
32,095
x \neq 0 \Rightarrow 1 = x/x
-3,613
5/4\cdot n = \frac{5}{4}\cdot n
6,662
-8 = \left(\cos(\pi) + i\sin(\pi)\right) \cdot 8
-19,587
\frac{\dfrac14}{\dfrac{1}{5}*9}*7 = 5/9*\frac{7}{4}
-19,997
\frac{1}{12 \cdot t + 16} \cdot (-54 \cdot t + 72 \cdot (-1)) = \frac{1}{6 \cdot t + 8} \cdot (6 \cdot t + 8) \cdot (-\frac92)
15,351
\cos(z + y) = -\sin{z}\times \sin{y} + \cos{z}\times \cos{y}
-10,323
\frac{4 \cdot (-1) + x}{x \cdot 10} \cdot \frac22 = \frac{1}{x \cdot 20} \cdot (8 \cdot (-1) + 2 \cdot x)
-1,445
7/6 \cdot \tfrac52 = \frac{5 \cdot \frac12}{1/7 \cdot 6}
5,801
24*(-1) + 72 = 48
2,024
k^2 \cdot k + k^2 + k \cdot 2 + 1 = k^3 + (k + 1)^2
-12,105
\frac{1}{9}\times 5 = \dfrac{x}{6\times \pi}\times 6\times \pi = x
13,048
D = x_2 \cap \dfrac{D}{x_1} = \frac{1}{x_1}\cdot D\cdot D/(x_2)
7,023
ba^2 = ba a
6,323
\frac{1}{-(-3\cdot t + 1) + 8}\cdot (5 - t) = 3 rightarrow -8/5 = t
2,958
\frac{3}{\sqrt{5}\times \dfrac15} = 15/\left(\sqrt{5}\right)
17,525
22 - 4 \cdot \left(16 + 21 \cdot (k + (-1)) + (-1)\right) = 42 - 84 \cdot k = 21 \cdot (2 - 4 \cdot k)
19,732
s + 0*\left(-1\right) = s
30,786
0 = {0 \choose 1}
16,921
10*x = \dfrac{\left(-20\right)*x}{-2} = -0.5*(-20*x)
11,313
\left((-1) + 2^l\right) \cdot 2 - 2^l l = -(l + 2(-1)) \cdot 2^l - 2
35,608
w^V = w^V
-7,149
\frac{3}{11}\cdot 3/12 = \frac{3}{44}
41,345
\frac{1}{4} = \frac{1}{6} + 1/12
-26,573
16 - z \cdot z \cdot 49 = 4 \cdot 4 - (z \cdot 7)^2
-1,589
π\cdot 7/4 = -\frac{π}{4} + 2\cdot π
3,586
0.0625 \cdot 0.8888 = 0.0625 \cdot \left(0.0001 + \dots + 0.1111\right)
23,553
\left(-x + 1\right)\cdot (1 + x) = 1 - x^2
-3,648
120/144 \dfrac{k^4}{k^3} = \dfrac{1}{144 k^3} 120 k^4
24,324
\frac{18}{3\times \left(1 + 5 + 4\times (-1)\right)} = 3
17,468
b^{d + c} = b^c*b^d
-5,058
\frac{1}{100}\cdot 87 = \dfrac{87}{100}
8,459
\frac{\mathrm{d}}{\mathrm{d}y} \sqrt{y} = 1/(2\sqrt{y})
37,562
\binom{n}{i}*i = n*\binom{n + (-1)}{(-1) + i}