id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
15,151 |
(3 - \sqrt{2})^4 = ((3 - \sqrt{2}) \times (3 - \sqrt{2}))^2 = (11 - 6\times \sqrt{2})^2 = 193 - 132\times \sqrt{2}
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-17,302 |
\frac{1}{100}\cdot 39.7 = 0.397
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14,708 |
100 \left(-24\right) + 49*49 = 1
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-13,742 |
\frac{27}{7 + 4(-1)} = 27/3 = 27/3 = 9
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-15,150 |
\tfrac{1}{x^{10}\cdot g^{20}\cdot x} = \dfrac{1}{x\cdot (x^2\cdot g^4)^5}
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18,766 |
-f^3 + a^3 = \left(f^2 + a^2 + f \cdot a\right) \cdot \left(a - f\right)
|
-1,762 |
2/3\cdot \pi = -\pi/12 + \frac{1}{4}\cdot 3\cdot \pi
|
24,183 |
10 + \cdots + 80 = 360
|
4,236 |
(g + b) \cdot \left(-b + g\right) = -b \cdot b + g^2
|
18,197 |
(x^2 + (-1))^3 = x^6 - 3x^4 + 3x \cdot x + (-1)
|
27,170 |
8!/(2!\times 3!) = 8\times 7\times 6\times 5\times 2 = 3360
|
34,710 |
\mathbb{E}[-Y + l] = -\mathbb{E}[Y] + l
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16,095 |
3\cdot 2\cdot 3 = 2 \cdot 2 \cdot 2 + 3^2 + 1
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36,001 |
1/(G*A) = 1/(G*A)
|
2,871 |
1/(d h) = \tfrac{1}{h d}
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-9,207 |
-y*4 - y^2*12 = -2*2*3*y*y - 2*2*y
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-22,986 |
\dfrac{10 \cdot 14}{7 \cdot 14} = \frac{140}{98}
|
594 |
det\left(E_1 G + E_2\right) = det\left(E_2 + GE_1\right)
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-3,753 |
64/88*\dfrac{y^2}{y^5} = \frac{64*y^2}{y^5*88}
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29,349 |
250/3 = -125/3 + 125
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14,687 |
5 \cdot x + y = d/dx (y^3 \cdot 5) + x^2
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-29,557 |
4\cdot x^3/x - x\cdot 3/x + \frac1x = (4\cdot x^2 \cdot x - 3\cdot x + 1)/x
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18,565 |
\frac{1}{2}\frac{5}{2}\cdot 5=\frac{25}{4}
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31,354 |
|x| = \|\left(x + y\right)/2 + \dfrac{1}{2} (x - y)\| \leq (|x + y| + |x - y|)/2
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10,407 |
234 = 66 (-1) + 300
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6,434 |
(2 + 1 + 5 + 8 + 1 + 1)/6 = 3
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2,302 |
k!\cdot \left(k! + (-1)\right)\cdot (k! + 2\cdot (-1))\cdot ...\cdot 2 = (k!)!
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4,803 |
-2 \cdot b \cdot a + (b + a) \cdot (b + a) = b^2 + a^2
|
6,270 |
x^{1/2} Z x^{\frac{1}{2}} = xZ
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-10,381 |
-40 = 40\cdot d + 30\cdot (-1) + 6 = 40\cdot d + 24\cdot (-1)
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19,100 |
1 + a^2\cdot 3 - a\cdot 4 = (\left(-1\right) + a)\cdot (3\cdot a + (-1))
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13,854 |
Z_i*Z_j = Z_j*Z_i
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2,504 |
5\times A = -5\Longrightarrow A = -1
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11,051 |
1 + s^4 = (s^2 + 1) \cdot (s^2 + 1) - 2s^2
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54,637 |
10=4+2+1+1+1+1
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5,715 |
9^{m + 1} + 9 \times (-1) = ((-1) + 9^m) \times 9
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20,543 |
p \cdot p + (-1) = (1 + p)\cdot 2\cdot \frac{1}{2}\cdot (p + (-1))
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-6,556 |
\frac{3}{(y + 3\cdot \left(-1\right))\cdot (9\cdot \left(-1\right) + y)} = \dfrac{3}{y^2 - 12\cdot y + 27}
|
30,513 |
-\frac{x}{-2} = \dfrac{1}{-2}*((-1)*x) = x/2
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23,355 |
5\cdot (-1) + 2\cdot n^3 \geq n^3\Longrightarrow n^3 \geq 5
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-27,772 |
d/dy (-4 \cdot \cot(y)) = -4 \cdot d/dy \cot(y) = 4 \cdot \csc^2(y)
|
26,982 |
-\sin{\frac{\pi}{3}} = \sin{4\cdot \pi/3}
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-18,948 |
\dfrac{3}{10} = \dfrac{A_s}{64\pi} \times 64\pi = A_s
|
51,844 |
3\cdot 6 + 1 = 19
|
13,344 |
1 + 2 \cdot n = -n^2 + (n + 1)^2
|
12,507 |
\left(-1\right) + x^2 = (x + (-1)) \cdot \left(x + 1\right)
|
14,509 |
r*s*w = w*s*r
|
-3,147 |
\sqrt{13} \cdot (3 + 1) = 4 \cdot \sqrt{13}
|
6,387 |
g^2 - c^2 = \left(g + c\right)\cdot (-c + g)
|
-3,572 |
\frac{t}{t^2} = \dfrac{1}{t\cdot t}\cdot t = \frac{1}{t}
|
2,534 |
\left(\tfrac{a\cdot g}{a}\cdot 1\right)^x = \frac{a}{a}\cdot g^x
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-5,744 |
\frac{3}{(9 \cdot (-1) + r) \cdot 4} = \frac{1}{r \cdot 4 + 36 \cdot (-1)} \cdot 3
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33,547 |
9828 = 2^2 \cdot 3^3 \cdot 7 \cdot 13 = \frac{1}{2 \cdot 26 \cdot 27 \cdot 28} = \frac{1}{2(3^3 + \left(-1\right)) \cdot 3^3 \cdot \left(3 \cdot 3^2 + 1\right)}
|
21,998 |
|d*A| = |A| = |A*d|
|
10,593 |
\left(x\cdot 2 + d = (-1) - 3\cdot x^3 + 2\cdot x \implies d + 1 = -3\cdot x^3\right) \implies \left(1 + d\right)/\left(-3\right) = x^3
|
-7,571 |
\frac{-i \cdot 18 + 6}{-2i + 4} = \frac{6 - 18 i}{4 - i \cdot 2} \dfrac{4 + 2i}{4 + 2i}
|
12,160 |
\frac{2^3*3^4}{5^4} = \frac{648}{625} \gt 1
|
2,882 |
(-\sqrt{2} + 2)\cdot (5 + \sqrt{2}) = (2 + \sqrt{2})\cdot (-7\cdot \sqrt{2} + 11)
|
8,250 |
\tanh{z_2} = \tanh{z_1} rightarrow z_2 = z_1
|
8,046 |
(1 + 10^{n + 1}*8)/9 = 8*(10^{1 + n} + \left(-1\right))/9 + 1
|
1,059 |
\frac{1-\dfrac1t}{t-1}=\frac1t
|
28,053 |
(1 + x) \cdot l \cdot \beta - \left(l - q\right) \cdot \beta = l \cdot \beta + x \cdot l \cdot \beta - l \cdot \beta + q \cdot \beta = (x \cdot l + q) \cdot \beta
|
-27,712 |
-2 \cdot \sin\left(x\right) = d/dx (2 \cdot \cos\left(x\right))
|
-25,349 |
\sin\left(x\right) x\cdot 2 + x^2 \cos(x) = d/dx (x^2 \sin(x))
|
5,866 |
(3 + g) (1 + g) = 3 + g^2 + 4g
|
28,032 |
|k| \cdot |\mu| = |k \cdot \mu|
|
-18,441 |
\dfrac{q}{(5 (-1) + q) \left(q + 6 (-1)\right)} \left(q + 5 (-1)\right) = \frac{-q*5 + q^2}{q^2 - q*11 + 30}
|
3,629 |
16*k^2 + k^2*x^2 + 8*k^2*x = -x^2 + 16 \Rightarrow (\left(-1\right) + k * k)*16 + x^2*(k * k + 1) + 8*x*k^2 = 0
|
-7,010 |
\frac{1}{13}\cdot 2\cdot \dfrac{6}{14} = 6/91
|
51,623 |
2\cdot 7 + 6 = 20
|
11,777 |
\left\{Y_1, Y_2\right\} \Rightarrow Y_2 = Y_1 \cup Y_2
|
404 |
1 + \sqrt{5} = (a + b\times \sqrt{5})\times (f + d\times \sqrt{5}) = a\times f + 5\times b\times d
|
8,851 |
\cos^2{x} = (\cos{2*x} + 1)*\frac{1}{2}
|
21,542 |
\frac{(3\cdot n + 1)^{1 / 2}}{(3\cdot n + 1)^{\frac{1}{2}}} = 1 \neq \frac{1}{3\cdot n + 1}\cdot (3\cdot n + 1)^{\dfrac{1}{2}}
|
13,190 |
A \cdot C \cdot C = 16 + 9 + 6 \cdot \left(-1\right) = 19 \Rightarrow 19^{1/2} = C \cdot A
|
9,407 |
\frac{11}{36} = \frac{1}{6} + \dfrac{5}{6}*1/6
|
7,791 |
120 = \frac{15}{2}\times 16
|
4,671 |
\left\{E, F\right\} \implies E \cup F \setminus E = F
|
24,630 |
A \cdot X = 0\Longrightarrow 0 = A\text{ or }0 = X
|
16,428 |
\left(-1\right) + x^3 = \left(4 + x\right) (x^2 - 4x + 3) + 13 (x + (-1))
|
1,606 |
a^{(-1) + b} = \frac{a^b}{a}
|
11,685 |
\frac{1}{w^2 + 5} + 4 = \frac{1 + 4(w^2 + 5)}{w^2 + 5} = \frac{1}{w^2 + 5}(4w * w + 21)
|
17,796 |
2^k = (1 + k) \cdot (k + 2) \cdot \dots \cdot 2 \cdot k
|
14,777 |
\cos{kx} + i\sin{kx} = e^{ikx} = (\cos{x} + i\sin{x})^k
|
9,730 |
-\sin^2\left(x\right) \cdot 2 + 1 = \cos(2 \cdot x)
|
33,269 |
\frac{17}{5} = 2/5 + 3
|
-1,967 |
\dfrac{1}{4} \cdot \pi + \pi = 5/4 \cdot \pi
|
23,201 |
\left(3/5\right)^2 + (\dfrac45)^2 = 1
|
21,136 |
25^{2 + n} = 5^{2*n + 4}
|
8,567 |
(1 + 6\cdot b)\cdot (6\cdot m + 1) = 1 + 6\cdot \left(m + m\cdot b\cdot 6 + b\right)
|
-25,789 |
\tfrac{4}{8 \cdot 5} = \dfrac{1}{40} \cdot 4
|
33,715 |
1/2 + 0 = 2/4 < \dfrac{2}{\pi}
|
14,854 |
a\cdot (1 - i) - x = 0 \Rightarrow a = \dfrac{1}{2}(i + 1) x
|
12,637 |
6\cdot 5^k + 6\cdot (-1) - 5^k + 5 = 5^k\cdot \left(6 + (-1)\right) + \left(-1\right)
|
32,541 |
5/8 = -1/8 + \frac{1}{2} + 1/4
|
29,813 |
(6 + j^3 + 3\cdot j \cdot j + 8\cdot j)/3 = ((j + 1)^3 + 5\cdot (1 + j))/3
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-23,289 |
1 - 3/7 = \frac{4}{7}
|
-16,415 |
7\sqrt{16} \sqrt{11} = 7*4 \sqrt{11} = 28 \sqrt{11}
|
29,258 |
2^2 \cdot 179 = 716
|
19,836 |
1 + y + y^2 + y^3\cdot \ldots = \frac{1}{1 - y}
|
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