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ddrg
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math_formulas

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int64
-30,985
55.9k
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16,321
\left(\dfrac{x^{\sigma}}{x}\right)^{\sigma} = (\dfrac1x)^{\sigma}\times x = \frac{1}{1/x\times x^{\sigma}}
28,963
0 = E(X^4) \implies E(X \cdot X) = 0
-9,326
p \cdot 2 \cdot 2 \cdot 2 = p \cdot 8
-25,807
\frac{1 \cdot 2}{7 \cdot 6} = 2/42
24,009
9 \cdot (-1) + 2 \cdot 10 = 11
31,918
(-4\cdot z + 8)/2 = -z\cdot 2 + 4
722
5 \cdot 5 + 5^2 = 1 \cdot 1 + 7^2
31,446
151200 = \frac{7!\cdot 6!}{2!\cdot 3!\cdot 2!}
9,610
(c + g\cdot i)\cdot (c - g\cdot i) = c^2 - g^2\cdot i \cdot i = c^2 + g \cdot g
22,946
125/6\cdot \tfrac34 = \frac{125}{8}
-16,370
117^{\frac{1}{2}} \cdot 5 = \left(9 \cdot 13\right)^{1 / 2} \cdot 5
5,711
b\cdot z + a = a + b\cdot z
-11,467
i \times 12 + 0 + 20 \times (-1) = -20 + 12 \times i
7,350
(x * x - x*6 + 13) (1 + x) = 13 + x^3 - x * x*5 + 7x
5,367
16 + x * x^2 - 12*x = \left(x * x + 2*x + 8*(-1)\right)*(x + 2*(-1))
-3,659
5*\frac16/s = \dfrac{5}{6*s}
16,201
\frac{((-1) + p)!}{p + \left(-1\right)} = (2 \cdot \left(-1\right) + p)!
-20,017
\tfrac{1}{-14}\cdot (b\cdot 7 + 42\cdot (-1)) = 7/7\cdot \frac{1}{-2}\cdot \left(b + 6\cdot \left(-1\right)\right)
36,786
x \cdot x + I = x^2 + x \cdot x + x + I = x + I
-22,711
\frac{1}{77} \cdot 110 = \frac{110}{11 \cdot 7} \cdot 1
30,866
\tfrac26 = \frac13
10,172
\frac{1}{\left(y + (-1)\right)\cdot (y + \left(-1\right))} = \dfrac{1}{(\left(-1\right) + y)\cdot (y + (-1))}
-26,477
2 \times 7 \times x \times 5 = 70 \times x
44,460
2\cdot x + 5 + 3 = 2\cdot x + 8 = 46 + 3\cdot x
-4,512
\frac{1}{x^2 - x + 12\cdot \left(-1\right)}\cdot (20 + 2\cdot x) = -\frac{2}{x + 3} + \dfrac{4}{x + 4\cdot (-1)}
26,494
-t^2 + d^2 = (d - t)\cdot \left(t + d\right)
-30,931
90 = 15\cdot 3\cdot 2
-3,924
\frac{6 \cdot t^4}{22 \cdot t^5} \cdot 1 = \dfrac{1}{t^5} \cdot t^4 \cdot \frac{6}{22}
26,672
1 = -2 \cdot 2^2 + 3^2
18,103
\dfrac72\cdot 2 = 7
7,669
-(k - t)\cdot 4 = \left(-k + t\right)\cdot 4
47,183
S + S = S\cdot 2
32,569
\frac{1}{2}*3*6 = 9
-7,410
6/10\cdot \frac{2}{9} = \frac{2}{15}
24,227
(-1) + y^{10} = (y + 1)*(y^8 + y^6 + y^4 + y^2 + 1)*\left(y + (-1)\right)
-20,944
-\frac{36}{81} = -4/9*\dfrac{9}{9}
663
2^k + (-1) = \frac{1}{1 + 2 (-1)} (1 - 2^k)
8,455
\frac{1}{3} = 0.33333\cdot \ldots
-22,725
35/15 = \dfrac{7}{3*5}*5
22,917
-(2 + \frac{1}{5} \cdot 3) = -\dfrac{3}{5} - 2
27,190
2^{n + (-1)}*2^{n + (-1)} = 2^{n + (-1)} * 2^{n + (-1)} = 2^{2*(n + (-1))} = (2^2)^{n + (-1)}
-7,839
\frac{1}{4 - 5 \cdot i} \cdot (-1 + 32 \cdot i) \cdot \frac{4 + 5 \cdot i}{i \cdot 5 + 4} = \tfrac{32 \cdot i - 1}{4 - 5 \cdot i}
10,180
((-1) + x) (1 + x) = \left(-1\right) + x \cdot x
14,879
y + 2\cdot (-1) + i = y - 2 - i
4,556
y \geq z,y \leq z\Longrightarrow y = z
-20,153
-\frac{1}{2} 7 \frac{1}{r \cdot (-3)} (r \cdot \left(-3\right)) = \frac{r \cdot 21}{r \cdot (-6)}
-20,437
\dfrac{15}{-3} = -3/(-3) (-\frac{1}{1} 5)
11,310
z^2 = 1 + (1 + z) \cdot (z + (-1))
36,161
16 = 4 \times 2 + 2 \times 4
21,973
x^2 + \frac{1}{x^2} + 2 \cdot (-1) = \frac{1}{x^2} \cdot (x^4 - 2 \cdot x^2 + 1) = \dfrac{1}{x^2} \cdot (x \cdot x + (-1)) \cdot (x \cdot x + (-1))
28,445
1 + t^2 + t/4 = (t + 1/8)^2 - 1/64 + 1
37,811
\frac18\cdot \sqrt{24} = \frac{2\cdot \sqrt{6}}{8}\cdot 1 = \dfrac{\sqrt{6}}{4} = \sqrt{6}/4
-12,128
31/36 = s/\left(18 \pi\right) \cdot 18 \pi = s
-4,415
4 + x \cdot x + x \cdot 5 = \left(1 + x\right) \left(x + 4\right)
3,940
\sum_{i=3}^n i \cdot i = \sum_{i=1}^n i \cdot i - 1^2 + 2 \cdot 2 = \sum_{i=1}^n i^2 + 5 \cdot (-1)
6,253
d/dx \operatorname{asin}(x) = \frac{1}{\sqrt{-x \times x + 1}}
501
0 = z*x + x*y'' + y'*2 rightarrow y''*x * x + x*y'*2 + x^2*z = 0
11,862
6*n + 3 = (1 + 2*n)*3
12,887
x + 5 - 4/(-1) = \frac{1}{1 \cdot \left(1 + 2 \cdot (-1)\right)} \cdot (7 + 2) \cdot (2 + 5 \cdot (-1)) \Rightarrow x = 18
33,176
\frac{1}{Y + 2 + \lambda_j}(2 + 2Y) = -\frac{-Y + \lambda_j}{Y + 2 + \lambda_j} + 1
-15,684
\dfrac{{(z^{3}p^{3})^{-3}}}{{(z^{5}p^{-3})^{-1}}} = \dfrac{{z^{-9}p^{-9}}}{{z^{-5}p^{3}}}
-23,100
1/\left(4\cdot 16\right) = \frac{1}{64}
26,916
0 = 10\cdot \left(-1\right) + 4^1 + 6
13,937
4 + y^2 \cdot 36 + 24 \cdot y = (2 + y \cdot 6)^2
-12,737
\frac{1}{8.5}85 = 10
22,089
\frac{1}{2^x} \cdot 2^{2 \cdot x} = 2^{2 \cdot x - x} = 2^x
1,493
0 = \left(\lambda\times x - A\right)^2\times v_2 = (\lambda\times x - A)\times (\lambda\times x - A)\times v_2
52,446
{4n \choose 2n} = \frac{1}{(2n)!^2}(4n)! = \frac{(4n)!}{{2n \choose n}^2 n!^4}
-20,886
7/7 \cdot \dfrac{1}{a \cdot (-2)} \cdot (a + 9) = \frac{7 \cdot a + 63}{a \cdot (-14)}
31,925
A - X \cup Y = A \cap X \cup Y^c = X^c \cap (A \cap Y^c) = Y^c \cap \left(A \cap X^c\right) = A - X - Y
-9,322
18 - 42 r = -2*3*7 r + 2*3*3
7,059
\frac{1}{F_2\cdot F_1} = \tfrac{1}{F_2\cdot F_1}
35,739
1 = 2^x\Longrightarrow x = 0
21,963
1/2 + \frac13 + 1/12 = \dfrac{11}{12}
-5,462
\frac{1}{r*3 + 30}*2 = \tfrac{1}{\left(10 + r\right)*3}*2
2,050
-\pi/4 + 7\cdot \pi/12 = \dfrac{\pi}{3}
6,673
\cos{2 u} = \left(-1\right) + 2 \cos^2{u}
-23,104
-3\cdot (-\frac{1}{3}\cdot 4) = 4
-1,770
\dfrac32*\pi = \pi*\tfrac16*11 - \pi/3
-10,368
\frac{10}{10}*(-\frac{4*x}{x*2}*1) = -40*x/(x*20)
-8,369
-\frac{1}{3}6 = -2
1,707
\tan{A} = x \implies \tan^{-1}{x} = A
-23,348
1/3 = \frac19\cdot 4\cdot 3/4
654
1/8 + 3/8 = \frac{1}{2}
8,945
2 = (1 + \frac{1}{3}) \cdot \tfrac12 \cdot 3
27,790
\frac{1}{1/6\cdot 48} = 1/8
5,801
48 = 72 + 24 \cdot \left(-1\right)
36,311
a^{m + x} = a^m \cdot a^x
23,058
2^x |X^{|x|}| = |X^{|x|}| = |X|^{|x|}
23,803
E\left[X + x\right] = x + E\left[X\right]
9,048
\left( 5, 9, 0\right) = ( 2, 1, -5) + ( x, y, z)\Longrightarrow \left( 5, 9, 0\right) = ( x + 2, y + 1, z + 5\cdot (-1))
14,120
(2 g + 1) (2 g + 1) + 73 = 2\cdot (2 g^2 + g\cdot 2 + 37)
5,569
(b + a)^2 + (a - b) * (a - b) = (b^2 + a^2)*2
12,576
\tfrac{1}{F_1 \cdot F_2} = \frac{1}{F_2 \cdot F_1}
-24,278
\dfrac{19}{10 + 9} = \dfrac{19}{19} = 19/19 = 1
17,636
e^y = -y^2 + y*2 + 5\Longrightarrow e^y + y^2 - 2*y = 5
-19,306
3/2 \cdot \frac15 \cdot 8 = \frac{8 \cdot \dfrac{1}{5}}{\dfrac{1}{3} \cdot 2}
-24,356
9 + \frac{1}{10}\cdot 60 = 9 + 6 = 15
28,831
\frac{1}{\sinh(1)*2}*(e + 4) = \dfrac{e*4 + 1}{e^2 - 1} + 1
2,942
((-1) + z^2) (z * z + 3(-1)) = 3 + z^4 - 4z^2