id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-11,852 |
5.824 \times 0.01 = 0.058\;24
|
5,823 |
X^2\times X^2\times X^2 = X^6 = X^3\times X^3
|
45,998 |
1 = \frac{1}{(\pi \cdot 2)^{\frac{1}{2}}}\int\limits_{-∞}^∞ exp(\left((-1) x^2\right)/2)\,\mathrm{d}x rightarrow \int_{-∞}^∞ exp(\frac{1}{2}((-1) x^2))\,\mathrm{d}x = \pi^{1 / 2}
|
13,326 |
k^2 - 3/4 = \frac14\cdot (3\cdot (-1) + k^2\cdot 4)
|
1,957 |
6!/(2!*2!*2!) = \binom{4}{2}*\binom{6}{2}*\binom{2}{2}
|
-7,247 |
\frac{1}{5} 5 / 9 = 1/9
|
8,106 |
\frac12 = \frac{1}{3} + \dfrac{1}{6}
|
23,184 |
5/6*Z + \frac89*3*Z = \dfrac{5}{6}*Z + 16/6*Z = \frac{1}{2*Z}*7
|
8,949 |
(\sqrt{-2} - 1)*\left(-\sqrt{-2} + 1\right) = 1 + \sqrt{-2}*2
|
-15,843 |
-5\cdot \frac{9}{10} + 5/10 = -40/10
|
-1,242 |
\frac23*(-5/4) = (\frac14*\left(-5\right))/(3*1/2)
|
20,521 |
\frac{1}{1 + x} = \frac{1}{1 + x}\left(1 + x - x - x^2 + x \cdot x + x^2 \cdot x - x^3\right) = 1 - x + x^2 - \frac{x \cdot x \cdot x}{1 + x}
|
3,076 |
\frac{1}{132} \cdot (42 + 20) = \dfrac{31}{66}
|
52,716 |
0 \leq \dfrac{\sin^2{z}}{z^2} = \dfrac{1}{z^2}\cdot (1 - \cos{z})\cdot (1 + \cos{z}) \leq (1 + \cos{z})/2
|
3,028 |
0.333338 = (10^6 + 14)\cdot \frac{1}{3}/1000000 = \frac{1}{3}\cdot \left(1 + 14/1000000\right)
|
38,607 |
\dfrac{1}{1 - y} = 1 + y + y^2 + y^3 + y^4 + ...
|
6,066 |
\sin{x} = \frac{15}{17} \Rightarrow \frac{8}{17} = \cos{x}
|
1,130 |
95284 = \tfrac{84!}{3!*(84 + 3*(-1))!}
|
2,867 |
\frac{1}{2} = \frac{5 \cdot 1/32}{\frac{5}{32} + \dfrac{5}{32}}
|
-16,816 |
-7 = -7 (-2 t) - -56 = 14 t + 56 = 14 t + 56
|
22,333 |
\cos\left(y \cdot 2\right) = -\sin^2(y) \cdot 2 + 1
|
-14,249 |
8 + 4 \cdot 10 - 5 \cdot 9 = 8 + 40 - 5 \cdot 9 = 48 - 5 \cdot 9 = 48 + 45 \cdot \left(-1\right) = 3
|
33,974 |
\frac{11}{40} = \frac{275}{1000}
|
-25,843 |
h^5 = \frac{h}{h}\cdot h\cdot h\cdot h\cdot h\cdot h
|
6,048 |
(z + x)^2 = x^2 + x\cdot z\cdot 2 + z \cdot z
|
32,158 |
\frac{\left(j!\right)!}{((-1) + j!)!} = j!
|
16,160 |
\frac{a}{x} = c \implies a = x\cdot c = 0\cdot c = 0
|
-2,852 |
-\sqrt{6} + \sqrt{4\cdot 6} + \sqrt{9\cdot 6} = -\sqrt{6} + \sqrt{24} + \sqrt{54}
|
-20,092 |
-\frac{12}{28\cdot t + 4} = 4/4\cdot (-\frac{3}{7\cdot t + 1})
|
8,743 |
0 = A * A\Longrightarrow 0 = A
|
12,557 |
\frac{1}{\left(l + 1\right)!} \cdot l! = \frac{1}{(l + 1) \cdot l!} \cdot l! = \frac{1}{l + 1}
|
10,937 |
p^{(-1) + p} \cdot 2 = p^{p + \left(-1\right)} + p^{p + (-1)}
|
573 |
\left(\dfrac{1}{x} \cdot y = w \Rightarrow x \cdot w = y\right) \Rightarrow x \cdot \frac{\text{d}w}{\text{d}x} + w = \frac{\text{d}y}{\text{d}x}
|
-20,972 |
(2 - 9\cdot p)/10\cdot 7/7 = \frac{1}{70}\cdot (14 - 63\cdot p)
|
-15,337 |
\frac{x^{15}}{x^5*\frac{1}{q^4}} = \frac{x^{15}*\frac{1}{x^5}}{\frac{1}{q^4}} = x^{15 + 5*\left(-1\right)}*q^4 = x^{10}*q^4
|
-27,373 |
6*(-1) + 56 = 50
|
6,896 |
\left(m \cdot m = x \cdot x \Rightarrow 0 = m^2 - x^2\right) \Rightarrow 0 = (m + x) \cdot (m - x)
|
22,847 |
gcg = gcg = gc g
|
17,490 |
20 - s^2\cdot 16 + s\cdot 32 = -16\cdot \left(s^2 - s\cdot 2 - \dfrac14\cdot 5\right)
|
28,068 |
0 = e^{\sin(x y)} + x^2 - 2 y + (-1) \approx x y + x^2 - 2 y
|
-20,228 |
-\frac{18}{2 + 2\cdot z} = -\frac{9}{1 + z}\cdot \tfrac22
|
7,641 |
45/100 = (1 - \frac{10}{100})/2
|
19,728 |
x^2 = x^2 + 2 \cdot 0 + 0^2
|
-16,457 |
28^{1/2} \times 7 = 7 \times (4 \times 7)^{1/2}
|
3,199 |
x \cdot y \cdot \varepsilon = x \cdot \varepsilon = \varepsilon = x \cdot y \cdot \varepsilon
|
11,533 |
(1 - \frac{3}{100}) \frac{3}{100} = 0.0291
|
-3,918 |
\frac{66\cdot q^5}{q \cdot q\cdot 24} = \frac{1}{q^2}\cdot q^5\cdot \tfrac{66}{24}
|
22,457 |
f^2 = 4 \cdot f^2 - f \cdot f \cdot 3
|
258 |
\binom{k + x + (-1)}{x} = \binom{x + k + (-1)}{x}
|
19,667 |
\mathbb{E}\left(V*X\right) = \mathbb{E}\left(V\right)*\mathbb{E}\left(X\right)
|
32,504 |
\dfrac{1}{5}109 = \frac{218}{10}
|
27,684 |
\frac13(1 + 2) = 10 + 9(-1)
|
-13,694 |
6 + 8 \cdot 7 - 5 \cdot 2 = 6 + 56 - 5 \cdot 2 = 62 - 5 \cdot 2 = 62 + 10 \cdot \left(-1\right) = 52
|
24,212 |
x = \sqrt{2} + 2^{1/3}\Longrightarrow 2 = (-\sqrt{2} + x)^3
|
14,561 |
\dfrac{j}{j * j} = 1/j
|
19,347 |
-11\cdot 3 + 2\cdot 17 = 1
|
53,580 |
\sec^2(x)/\tan(x) = \frac{1}{\tan(x)}*(1 + \tan^2\left(x\right)) = 1/\tan(x) + \tan(x) = \cot(x) + \tan\left(x\right)
|
19,935 |
\dfrac{1}{24} \cdot (27 + 24 \cdot \left(-1\right)) = \frac{3}{24} = \frac{1}{8} = 12.5
|
32,862 |
0 = N * N - N + x\Longrightarrow (N - x)*N + x = 0
|
8,088 |
(x^4 + (-1)) \left(x^4 + 1\right) = x^8 + \left(-1\right)
|
39,704 |
(x + (-1))*(x^2 + x + 1) = x^3 + (-1)
|
26,959 |
\tfrac{1}{(n + 1)\cdot 2}\cdot (2 + n) = \frac{1 + n + 1}{2\cdot (n + 1)}
|
16,334 |
4\times k^2 = (2\times k)^2
|
-445 |
π \cdot \dfrac{5}{3} = 17/3 \cdot π - 4 \cdot π
|
-8,886 |
6^2 = 6*6
|
-18,011 |
6 = 92 + 86 \left(-1\right)
|
4,164 |
3\cdot \sqrt{3} = \left(\sqrt{3}\right)^3
|
-3,058 |
25^{1/2}\cdot 7^{1/2} - 7^{1/2}\cdot 4^{1/2} = 5\cdot 7^{1/2} - 2\cdot 7^{1/2}
|
27,988 |
-(n + \left(-1\right))^3 + n^3 = 3\cdot n \cdot n - n\cdot 3 + 1
|
31,477 |
(m \cdot 2 + 4)^2 + (2 \cdot m) \cdot (2 \cdot m) + (2 \cdot m + 2)^2 = 4 \cdot (5 + 3 \cdot m^2 + 6 \cdot m)
|
4,391 |
151200 = 7*6*5*10*9*8
|
-10,349 |
-9 = -s + 8 + 35\cdot (-1) = -s + 27\cdot \left(-1\right)
|
20,543 |
(p + 1)\cdot 2\cdot ((-1) + p)/2 = (-1) + p \cdot p
|
15,583 |
\frac{6\cdot 1/10}{\dfrac38 + \dfrac{6}{10}} = 8/13
|
11,351 |
\frac12 \cdot (m + 1) - m/2 = \dfrac12 = \dfrac{m}{2} - (m + (-1))/2
|
42,881 |
0.125 = \left(-1\right) \times 0.875 + 1
|
29,302 |
\frac{1}{5 + 4}4 = 4/9
|
-2,172 |
\pi - \pi*2/3 = \pi/3
|
-20,096 |
\frac{7}{6 \cdot (-1) + a} \cdot \dfrac17 = \dfrac{1}{42 \cdot (-1) + a \cdot 7} \cdot 7
|
-2,908 |
\sqrt{13}\cdot \sqrt{4} - \sqrt{13} = -\sqrt{13} + 2\cdot \sqrt{13}
|
18,963 |
5^l \gt 4^l = 2^{2*l} > 2^{l + 1} + 1
|
437 |
\left(h + g\right)\cdot (h + g) = h \cdot h + g\cdot h + g\cdot h + g^2
|
29,890 |
\dfrac{1}{\left(-1\right) + z} = \frac{(-1) + z}{\left(z + \left(-1\right)\right)^2}
|
19,589 |
2 \cdot (c_1 + c_2) = c_2 + c_1
|
-549 |
e^{6\times \frac{19}{12}\times i\times \pi} = (e^{19\times \pi\times i/12})^6
|
23,265 |
3 (-1) + 3 = 0
|
-12,250 |
17/18 = \frac{t}{6 \cdot \pi} \cdot 6 \cdot \pi = t
|
26,451 |
h\cdot f\cdot a + (h + a)\cdot (f + a)\cdot (f + h) = (a\cdot f + a\cdot h + h\cdot f)\cdot (f + a + h)
|
54,430 |
sin(a-\frac {3\pi}{2})=sin(-(\frac {3\pi}{2}-a))=-sin(\frac {3\pi}{2}-a)=-(-cos a)=cos a
|
3,131 |
-x^3 + x^4 = x^3\cdot (x + (-1))
|
13,467 |
2\cdot y^2 + 6\cdot y + 35 = 2\cdot \left(y^2 + 3\cdot y\right) + 35 = 2\cdot (y + \frac32)^2 + \frac{61}{2}
|
15,552 |
5 \times (z + 2) + 13 \times (-1) = z + 3 \times \left(-1\right) + 4 \times z
|
3,993 |
0 \leq Var[X] = \mathbb{E}[(X - \mathbb{E}[X])^2] = \mathbb{E}[X^2] - \mathbb{E}[X]^2
|
-5,857 |
\frac{2}{20 \cdot (-1) + 2 \cdot x} = \tfrac{1}{(10 \cdot \left(-1\right) + x) \cdot 2} \cdot 2
|
-19,385 |
\frac38 \cdot 3/5 = \frac{3 \cdot \frac{1}{8}}{5 \cdot 1/3}
|
21,277 |
2 = (\sqrt{3} + 1) \cdot (\sqrt{3} - 1)
|
5,788 |
1995^2 + 1995\cdot f = 1995\cdot (f + 1995)
|
-12,752 |
10 = 7*(-1) + 17
|
2,340 |
(m + 1)^3 = 1 + m^3 + 3\cdot m \cdot m + 3\cdot m
|
15,663 |
\sin(-y + \dfrac{1}{2}\cdot \pi)\cdot \sin(y) = \cos(y)\cdot \sin\left(y\right)
|
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