id
int64 -30,985
55.9k
| text
stringlengths 5
437k
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|---|---|
-26,463 |
(-3*x + 2)^2 = 2^2 - 3*x*2*2 + (x*3)^2
|
20,023 |
m\cdot q + m + (-1) = m\cdot \left(1 + q\right) + (-1)
|
14,010 |
(x + 1 + I)\cdot (x + 1 + I) = x^2 + 2\cdot x + 1 + I = x + x \cdot x + x + 1 + I = x + I
|
20,666 |
\frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{x} = -\dfrac{1}{x^2} = -\dfrac{1}{x^2}
|
29,049 |
\left(n + (-1)\right) \cdot 2 + 1 = \left(-1\right) + n \cdot 2
|
4,687 |
\operatorname{Var}(V) = \operatorname{Var}(V_1 + \dotsm + V_{10}) = \operatorname{Var}(V_1) + \dotsm + \operatorname{Var}(V_{10})
|
-23,426 |
\frac{\dfrac15}{2}*4 = \frac{1}{5}*2
|
11,715 |
aE = Ea
|
39,663 |
1 + \tan(x)/x = \frac{1}{x}*(x + \tan(x))
|
-22,319 |
12 + n * n - n*8 = (n + 2*(-1))*(n + 6*(-1))
|
24,213 |
-45 \cdot 5 + 1140 + 120 \cdot (-1) = 795
|
29,425 |
10 \cdot (-1) + (-1) = -11
|
-1,304 |
7*\frac16/((-7)*1/4) = 7/6 (-\dfrac47)
|
-27,850 |
\frac{\mathrm{d}}{\mathrm{d}y} \csc(y) = -\cot(y)\cdot \csc\left(y\right)
|
9,905 |
(-2^k + 2)/\theta = -2^k/\theta + 1/\theta + \frac{1}{\theta}
|
-5,618 |
\frac{2}{2 h + 16 \left(-1\right)} = \frac{1}{\left(h + 8 (-1)\right)\cdot 2} 2
|
21,613 |
\frac{1}{4\cdot 2}(-4 + \sqrt{16 + 64 (-1)}) = \frac12(-1 + \sqrt{-3})
|
14,537 |
\overline{v \times x} = \overline{x} \times \overline{v}
|
9,339 |
\beta \lt -\alpha\Longrightarrow -\beta \gt \alpha
|
27,266 |
rrx = r^2 x
|
5,240 |
1 = \frac{1}{4} + 3/4
|
3,566 |
12\cdot \frac{\dfrac{1}{\sqrt{3}}\cdot 2}{\sqrt{2}} = 24/(\sqrt{6})
|
3,036 |
0 + x^3 + x \cdot x + x \cdot 0 = (x + 0)^2 \cdot (x + 1)
|
-6,695 |
50/100 + 3/100 = \frac{5}{10} + \dfrac{1}{100} \cdot 3
|
31,920 |
\frac{6}{(2 + 1)*2} = 1
|
-30,853 |
\frac{x^3 - 9\cdot x}{-3\cdot x + x^2} = 3 + x
|
3,144 |
\sin^2{x} = \left(-\cos{2*x} + 1\right)/2
|
16,733 |
(n*2 + n * n) \frac{5}{6} = \tfrac{1}{6}5 ((1 + n)^2 + (-1))
|
-15,234 |
\frac{1}{\dfrac{1}{x^5}\cdot a \cdot a\cdot \frac{1}{x^8}} = \frac{x^8}{a^2\cdot \frac{1}{x^5}}
|
8,151 |
S^2 - 2\cdot S + 3\cdot \left(-1\right) = (S + 3\cdot (-1))\cdot (1 + S)
|
-17,243 |
-29/3 = -\dfrac{29}{3}
|
14,648 |
-\frac{x}{x + 1} + 1 = \frac{1}{x + 1}
|
9,708 |
-1*\left(23 - 7*3\right) + 3 = 3 - 23 - 21
|
1,842 |
2/3 = \frac{2}{3}*0 + \frac13 + 1/3
|
-6,329 |
\frac{2}{10 \cdot (-1) + m} \cdot \frac{m + 1}{m + 1} = \frac{2}{(10 \cdot (-1) + m) \cdot \left(m + 1\right)} \cdot (m + 1)
|
-19,473 |
\frac{\dfrac{1}{7}}{3}\cdot 8 = \frac{1}{3\cdot \frac{1}{8}\cdot 7}
|
28,291 |
-\cos(h) = \cos(h + \pi)
|
48,064 |
16\cdot 11 = 176 = 7\cdot 25 + 1
|
412 |
\sin(2\cdot q - q) = \sin{q}
|
30,740 |
\frac{1}{y - x} = \frac{1}{(1 - \frac1y \cdot x) \cdot y}
|
6,578 |
h_1 n_1 n_2 h_2 = n_1 n_2 h_2 h_1
|
-6,252 |
\dfrac{1}{x^2 - x*3 + 18 (-1)}4 = \tfrac{1}{(x + 3) (x + 6(-1))}4
|
14,411 |
3 \leq y \implies e^{y + (-1)} > 2^{y + (-1)} \geq 2^{y + \left(-1\right)} = \left(1 + 1\right)^{y + \left(-1\right)}
|
25,467 |
\frac{1}{2} \cdot \left(1 - \cos{2 \cdot x}\right) = \sin^2{x}
|
11,533 |
3/100\cdot (1 - \frac{3}{100}) = 0.0291
|
16,161 |
-\frac16\cdot 3 = -1/2
|
3,168 |
I = (I - B) \cdot (C + I) = C + I - B \cdot C - B
|
-4,284 |
\frac{z^3}{z * z} = z*z*z/(z*z) = z
|
23,948 |
123456789=3^2\times3607\times3803
|
-7,600 |
\left(12 - 28 i + 12 i + 28\right)/8 = (40 - 16 i)/8 = 5 - 2i
|
-29,592 |
\frac{d}{dx} (2\cdot x^2) = 2\cdot \frac{d}{dx} x \cdot x = 2\cdot 2\cdot x^1 = 4\cdot x
|
22,232 |
\frac{11}{50} = 13/26 \cdot 2 \cdot 12/25 \cdot 11/24
|
8,567 |
6 \cdot (m \cdot n \cdot 6 + n + m) + 1 = (6 \cdot m + 1) \cdot (1 + 6 \cdot n)
|
18,285 |
1 - \cos\left(u\right) = 2 \sin^2(\dfrac{u}{2}) \leq u^2/2
|
23,855 |
\dfrac16 * \left(\dfrac16\right)^2 = 1/216
|
26,520 |
-y^4 + x^4 = (x + y) \left(-y + x\right) (x^2 + y * y)
|
14,573 |
12^2 = (2^2*3)^2 = 2^4*3^2
|
16,797 |
(p-2x)^2 = p^2-4px+4x^2
|
12,712 |
(-1) + (k + 1)*k!*\left(2 + k\right) = (2 + k)*k!*(k + 1) + (-1)
|
-3,951 |
\frac{44 \cdot a^5}{a^5 \cdot 55} \cdot 1 = \frac{1}{55} \cdot 44 \cdot \dfrac{1}{a^5} \cdot a^5
|
-3,125 |
5 \sqrt{2} = \sqrt{2} \cdot ((-1) + 2 + 4)
|
2,211 |
\dfrac{1}{6} = 0.166666\cdot \ldots
|
10,174 |
3^k + (-1) = 2 \cdot 3^0 + 3^1 \cdot 2 + 2 \cdot 3^2 + \cdots + 2 \cdot 3^{k + \left(-1\right)}
|
12,587 |
46 = 15 + 5*0 + 4*2 + 3*3 + 2*7
|
3,018 |
\dfrac{2}{2}\cdot 20\cdot 4 = 20\cdot 4 = 80
|
25,353 |
-7/24 = \cot{\alpha} \implies \tan{\alpha} = -24/7
|
13,547 |
1/(\frac{1}{d_1} d_2) = d_1/(d_2) = 1/(\dfrac{1}{d_2} d_1)
|
5,542 |
\cot(-\frac{37}{2} \cdot \pi) = 0
|
-9,121 |
63\cdot x - 7\cdot x^2 = -7\cdot x\cdot x + x\cdot 3\cdot 3\cdot 7
|
-21,006 |
-\dfrac{2}{3}\cdot \frac{6\cdot (-1) - z}{6\cdot (-1) - z} = \dfrac{12 + 2\cdot z}{-z\cdot 3 + 18\cdot (-1)}
|
8,622 |
-f'' = f''*i^2
|
-6,687 |
\frac{1}{100}4 + 4/10 = 4/100 + \frac{40}{100}
|
30,113 |
\sqrt{6}\cdot 2 + 5 = \dfrac{1}{-2\cdot \sqrt{6} + 5}
|
22,130 |
\binom{19}{2}\cdot \binom{1}{1}/(\binom{20}{3}) = \frac{3}{20}
|
52,571 |
(x^2 - y^2) \times (x^2 - y^2) + \left(2 \times x \times y\right)^2 = x^4 - 2 \times x^2 \times y^2 + y^4 + 4 \times x^2 \times y^2 = x^4 + 2 \times x^2 \times y^2 + y^4 = (x^2 + y^2)^2
|
22,595 |
c = 3^0*c
|
-7,846 |
(-11 - 3 \times i - 22 \times i + 6)/5 = \frac15 \times (-5 - 25 \times i) = -1 - 5 \times i
|
6,363 |
\sin{2*x} = 2*\sin{x}*\cos{x} = \sin^2{x}
|
-10,726 |
-(p\cdot 8 + 10)/\left(2\cdot p\right) = \frac{2}{2}\cdot (-(4\cdot p + 5)/p)
|
21,560 |
(-y^2 + 2 \cdot 2)^{1/2} = h\Longrightarrow h \cdot h + y^2 = 2^2
|
-20,775 |
8/8\cdot \frac{2 - 6\cdot n}{n + 5\cdot (-1)} = \tfrac{-48\cdot n + 16}{n\cdot 8 + 40\cdot \left(-1\right)}
|
-12,428 |
58 = \dfrac{116}{2}
|
24,675 |
x^6 = (3*x^3)^2 + (-x * x*2)^3
|
8,973 |
L' - \dfrac{1}{1 + \sin{L'}}(L' - \cos{L'}) = L'
|
35,532 |
Cy = Cg y = gC y
|
2,882 |
(-\sqrt{2} + 2)*(5 + \sqrt{2}) = (\sqrt{2} + 2)*(-\sqrt{2}*7 + 11)
|
-174 |
\binom{9}{5} = \frac{9!}{5! \left(9 + 5 (-1)\right)!}
|
-19,013 |
1/2 = \frac{G_q}{16\cdot \pi}\cdot 16\cdot \pi = G_q
|
5,146 |
\dfrac{1}{q + 1} = 1 - q + q^2 - \frac{q \cdot q^2}{1 + q}
|
29,050 |
k * k * k + k^2*3 + 3*k + 1 = \left(1 + k\right)^2 * (1 + k)
|
-10,569 |
\frac{1}{25 \cdot y} \cdot 1 = \frac{3}{y \cdot 75}
|
12,162 |
\sin(z) = (e^{i*z} - e^{-i*z})/(2*i) = -i*\sinh(i*z)
|
25,028 |
x + s = (x + s) \cdot (x + s) \Rightarrow x \cdot s + x \cdot s = 0
|
-19,058 |
3/4 = \frac{A_s}{49*π}*49*π = A_s
|
-2,605 |
(16\cdot 11)^{1 / 2} - (4\cdot 11)^{\frac{1}{2}} = 176^{1 / 2} - 44^{\dfrac{1}{2}}
|
13,182 |
( x^2, x \cdot N) = ( x^2, N) \cap ( x \cdot x, x) = x \cap \left( x \cdot x, N\right)
|
5,966 |
1 - x \cdot x \cdot x = (x^2 + 1 + x) \cdot (1 - x)
|
12,973 |
-a + a + z = a + y - a rightarrow y - a + a = -a + a + z
|
22,763 |
4 = z^2 - x * x = (z - x)*(z + x)
|
3,437 |
400\cdot (1 + 0.25) = 500
|
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