id
int64 -30,985
55.9k
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stringlengths 5
437k
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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
|
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