id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
19,778 |
\frac{1}{\phi^2} = \frac{1}{\phi^2}\cdot (\phi^2 - \phi) = 1 - \tfrac{1}{\phi}\cdot \left(\phi \cdot \phi - \phi\right) = 2 - \phi
|
-19,208 |
\tfrac{1}{5} = \dfrac{X_q}{16\cdot \pi}\cdot 16\cdot \pi = X_q
|
10,131 |
5^3 + 5 + 6^3 + 6 = 7^3 + 7 + 2
|
26,550 |
\tfrac{(-1) + y^{\dfrac{1}{2}}}{\left(-1\right) + y} = \frac{1}{1 + y^{1 / 2}}
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37,253 |
\frac27 = \tfrac{1}{7}\cdot 2
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-10,269 |
3/3\cdot \frac{p\cdot 3 + 2\cdot (-1)}{p\cdot 8 + 4\cdot \left(-1\right)} = \tfrac{9\cdot p + 6\cdot (-1)}{24\cdot p + 12\cdot (-1)}
|
8,430 |
x \times 2 + 2 \times y = 5.9\Longrightarrow y = \frac{1}{2} \times (-x \times 2 + 5.9)
|
25,959 |
\frac{251^2*250^2}{4} = 984390625
|
4,664 |
(c_2 - c_1)^2 = (c_2 + c_1)^2 - 4 \cdot c_2 \cdot c_1
|
307 |
r_1 \cdot 2 \cdot m \cdot r_2 = r_1 \cdot r_2 \cdot m \cdot 2
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-8,365 |
-32 = 8 \cdot \left(-4\right)
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-20,818 |
-\dfrac{2}{7} \cdot \frac55 = -\frac{1}{35} \cdot 10
|
-16,561 |
\sqrt{48} \times 9 = \sqrt{16 \times 3} \times 9
|
15,301 |
X = \operatorname{acos}(z) \Rightarrow \cos(X) = z
|
31,674 |
10\cdot \left((-1) + 3\right) = 20
|
31,661 |
108^{\frac{1}{2}} + 10 = 10 + 6\cdot 3^{\frac{1}{2}}
|
-2,824 |
10*6^{1/2} = 6^{1/2}*(5 + 1 + 4)
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31,661 |
\sqrt{108} + 10 = \sqrt{3} \cdot 6 + 10
|
9,963 |
5^{n + 1}*(4 + 1) = 5^{1 + n} + 5^{n + 1}*4
|
-24,665 |
\frac{6}{21} = \frac{2}{7 \cdot 3}3
|
10,193 |
f^3 = f\times f^2 = f = f
|
-3,419 |
\sqrt{2}\cdot 6 = (2 + 1 + 3)\cdot \sqrt{2}
|
23,381 |
\frac{\mathrm{d}}{\mathrm{d}z} \operatorname{atan}(z) = \frac{1}{z^2 + 1}
|
28,410 |
(1 - i)^1 + (1 + i)^1 = 2
|
-9,500 |
-r \times 10 = -r \times 2 \times 5
|
-2,447 |
45^{1 / 2} + 20^{\dfrac{1}{2}} = \left(9 \cdot 5\right)^{1 / 2} + \left(4 \cdot 5\right)^{\frac{1}{2}}
|
24,430 |
2^m = 2^m \cdot k + 1 > 2^m \cdot k
|
2,942 |
x^4 - x^2*4 + 3 = \left((-1) + x^2\right)*(x^2 + 3*\left(-1\right))
|
8,923 |
0 = x^6 - 4x^3 + (-1) \Rightarrow x^3 = 2 ± \sqrt{5}
|
10,150 |
-\cos\left(\pi/2 + \theta\right) = \sin{\theta}
|
7,386 |
A*x^2 = A*x^2
|
-16,596 |
7 \cdot \sqrt{16 \cdot 5} = 7 \cdot \sqrt{80}
|
3,145 |
t - \frac{t}{1 + t^2} = \dfrac{t^3}{1 + t \cdot t}
|
1,787 |
-2\cdot z_1 \lt -2\cdot z_2 \Rightarrow z_2 < z_1
|
25,767 |
-1/6 + 1/2 + 1 = \dfrac43
|
17,892 |
B = \overline{x}\cdot B = B\cdot x
|
-26,600 |
3y^2 + 147 (-1) = 3(y \cdot y + 49 (-1)) = 3\left(y + 7\right) (y + 7(-1))
|
-16,341 |
80^{\tfrac{1}{2}}*10 = 10*\left(16*5\right)^{\dfrac{1}{2}}
|
15,646 |
\tfrac{x + 2*(-1)}{4*(-1) + x * x} = \tfrac{1}{x + 2}
|
7,403 |
\mathbb{P}(x) = (x - d) \left(x - b\right) (x - c) = x^3 - (d + b + c) x \cdot x + (db + bc + cd) x - dbc
|
23,667 |
((-1) + p)\cdot ((-1) + p)\cdot ((-1) + p) = (-1) + p \cdot p \cdot p - 3\cdot p^2 + p\cdot 3
|
-26,421 |
\frac{x^F}{x^k} = x^{F - k}
|
7,777 |
-\frac{r}{3} + ((-1) \cdot r)/3 + r = r/3
|
31,494 |
2^2\cdot 3^3\cdot 5\cdot 7^2 = 26460
|
-2,288 |
\frac{1}{20} = -\frac{1}{20}7 + \frac{8}{20}
|
4,557 |
k \geq w \implies -w \geq -k
|
16,138 |
\tfrac{1}{z^3}\cdot z^2 = \frac1z
|
-22,937 |
\frac{81}{9\cdot 5}\cdot 1 = \frac{1}{45}\cdot 81
|
8,455 |
1/3 = 0.33333 \cdot ...
|
-2,659 |
\sqrt{3} \sqrt{4} + \sqrt{3} \sqrt{25} = \sqrt{3}*2 + \sqrt{3}*5
|
8,924 |
\dfrac{1}{(1 + n)^2} \cdot (n^2 + n \cdot 2 + 1 + (-1)) = \frac{1}{(n + 1)^2} \cdot ((-1) + (n + 1)^2)
|
10,423 |
5 = 4\cdot k^2 + 4\cdot k + 1 = (2\cdot k + 1)^2
|
24,249 |
r \times r = 2^2 + 5 = 9 \Rightarrow 3 = r
|
20,508 |
503\cdot 497=(500+3)(500-3)=500^2-3^2=250000-9=249991
|
44,177 |
36047571 = 696\cdot 109376 - 40078125
|
-5,000 |
17.4*10^9 = 17.4*10^{3 + 6}
|
-20,649 |
-\tfrac{10}{-5\cdot n + 2\cdot (-1)}\cdot \frac{8}{8} = -\frac{80}{-n\cdot 40 + 16\cdot \left(-1\right)}
|
1,639 |
3\cdot \lambda\cdot z_2^{\frac{1}{3}\cdot 4} = z_1^{1/3} \implies 9\cdot z_2^4\cdot \lambda^3 = z_1
|
-6,338 |
\tfrac{3}{(n + 7)*5} = \frac{3}{35 + 5*n}
|
18,836 |
h - l = -(-h + l)
|
9,678 |
f \times a_2 = f \times a_2
|
12,846 |
\frac12(1 + \sqrt{5}) = 1/2 + \frac{\sqrt{5}}{2}
|
37,733 |
\sin{y \cdot k} \cdot k/y = k^2 \cdot \frac{\sin{y \cdot k}}{k \cdot y}
|
5,506 |
544320 = \binom{9}{2}*\binom{7}{2}*6!
|
6,497 |
x + 1 + (x + 2\cdot (-1))^n < 2\cdot x^2 - x = x + 2\Longrightarrow 1 \gt (x + 2\cdot (-1))^n
|
3,692 |
\vartheta \cdot z + r \cdot z = (\vartheta + r) \cdot z
|
3,194 |
exp(A)*exp(S) = exp(A + S)
|
16,036 |
\frac{2^7}{1000} = 2^7\cdot 1/8/125 = \tfrac{1}{125}\cdot 2^4
|
11,144 |
\|z\|^2 = zz^T = zz^T
|
-20,682 |
\frac{4 - 2\cdot r}{-r\cdot 16 + 32} = \frac{1}{8}\cdot 1
|
24,894 |
0 = \dfrac{1}{120 \cdot \pi} \cdot (\sin{2 \cdot \pi} - \sin{0})
|
20,249 |
10 \cdot \frac{654321}{123456} = 6 \cdot 9 + (-1) + \frac{7}{123456} \cdot 6 \approx 53
|
16,943 |
2/10\cdot \frac{3}{10} = \frac{1}{100}\cdot 6
|
-15,167 |
\frac{x^5}{t^{10} x^{10}} = \frac{1}{\frac{1}{\dfrac{1}{t^{10}} \frac{1}{x^{10}}}}x^5
|
7,366 |
(\mathbb{E}[X'^2]\cdot \mathbb{E}[Y'^2])^{\frac{1}{2}} = \mathbb{E}[X'\cdot Y']
|
-30,858 |
\frac{1}{x^3 - x^2}\cdot (-x \cdot x\cdot 3 + x^4 + 2\cdot x^3) = x + 3
|
34,623 |
\frac{0.6}{0.4 \cdot 0.6} \cdot 0.4 \cdot 0.6 = 0.6
|
19,555 |
\dfrac{2}{5} = (1 - \frac{1}{3}) \cdot (1 - 1/4) \cdot (1 - 1/5)
|
8,677 |
(\alpha + \beta)^2 - \beta \alpha*4 = (\alpha - \beta)^2
|
796 |
h_1 + d + h_2 = d + h_2 + h_1
|
33,567 |
1 - \dfrac{n}{n \cdot 2 + 1} = \dfrac{1 + n}{n \cdot 2 + 1}
|
-3,023 |
(3 + 2)\cdot \sqrt{13} = 5\cdot \sqrt{13}
|
-20,777 |
\frac{p + 4}{4 + p}\cdot (-\frac{1}{7}\cdot 4) = \dfrac{1}{28 + 7\cdot p}\cdot \left(16\cdot \left(-1\right) - p\cdot 4\right)
|
10,486 |
1 = 2\times Q^3 + Q = Q\times (2\times Q \times Q + 1) = \left(Q^3 + 1\right)\times (2\times Q^2 + 1)
|
-28,892 |
\left(100 + 200 + 150 + 150\right)/4 = \frac14*600 = 150
|
-1,585 |
\dfrac{23}{12}\cdot \pi = -\pi/12 + \pi\cdot 2
|
-12,061 |
3/20 = \dfrac{s}{10 \cdot \pi} \cdot 10 \cdot \pi = s
|
-2,702 |
10^{\frac{1}{2}} \cdot (5 + 2 + (-1)) = 6 \cdot 10^{1 / 2}
|
4,587 |
5/18 = \frac{1}{216} \cdot 5/(1/12)
|
-16,885 |
-5 \cdot x = -5 \cdot x \cdot (-x) + -5 \cdot x \cdot 4 = 5 \cdot x^2 - 20 \cdot x = 5 \cdot x^2 - 20 \cdot x
|
17,745 |
\sin{x} = \sin\left(x + \pi \cdot 2\right)
|
28,637 |
\cos{\pi\cdot m\cdot 2} = \cos{6\cdot m\cdot \pi/3}
|
22,325 |
z*x*3/2 - \frac54 = -1/2 + 3/2*z*x - \frac14*3
|
3,985 |
(-x^2 + 1)/2 = \frac{1}{2}\cdot (1 + x)\cdot (-x + 1)
|
1,586 |
g x H = H x g
|
-1,593 |
\frac{4}{3}*π = 4/3*π + 0
|
39,734 |
12/27 = \dfrac{96}{6^3}\times 1
|
-9,456 |
t*2*2*2*3*5 + 2*2*3 = t*120 + 12
|
13,988 |
(h + x)*(h - x) = h * h - x^2
|
-20,838 |
-1/4 \frac{(-1) + q}{q + (-1)} = \frac{-q + 1}{4(-1) + 4q}
|
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