id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
4,937 |
b/c + a/c = \frac1c\cdot (b + a)
|
16,327 |
a_t + b_t = a_t + b_t
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20,836 |
-5 = 4*(-1) - 1
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-15,574 |
\frac{z^4}{\left(z^2\cdot t^2\right)^3} = \frac{z^4}{t^6\cdot z^6}
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15,807 |
-(x \cdot x^2 + 1) + (x + 1)^3 = 3 \cdot (x + x^2)
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33,998 |
2*13 * 13 = 338
|
18,805 |
1 - \cos{4 \cdot y} = (4 \cdot y)^2/2! + ... = 8 \cdot y^2 + ...
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15,351 |
\cos(x + y) = \cos{x} \cdot \cos{y} - \sin{y} \cdot \sin{x}
|
1,779 |
a^{1/2} \cdot a^{1/2} \cdot a^{1/2} = a^{3/2}
|
9,553 |
4 + \eta = v \Rightarrow \eta = v + 4 (-1)
|
-1,600 |
-\frac{5}{12}\cdot \pi + 2\cdot \pi = 19/12\cdot \pi
|
-22,899 |
\dfrac{56}{8 \cdot 10} \cdot 1 = 56/80
|
-23,942 |
7 + \frac{48}{8} = 7 + 6 = 13
|
3,410 |
(A + E)^2 = (A + E) (A + E) = A A + A E + E A + E^2 \neq A^2 + E^2
|
11,918 |
S \cdot T = (S^{1/2} \cdot T^{\frac{1}{2}})^2
|
20,036 |
(2 + \sqrt{3})*\left(2 - \sqrt{3}\right) = 2 * 2 - \sqrt{3} * \sqrt{3} = 1
|
30,811 |
\frac{1/3}{2} \cdot 2 = \dfrac13
|
43,381 |
286 = 12 \cdot 3 + 50 \cdot 5
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-4,580 |
\frac{-2 \cdot x + 8}{15 + x \cdot x - 8 \cdot x} = -\dfrac{1}{5 \cdot (-1) + x} - \frac{1}{x + 3 \cdot \left(-1\right)}
|
-11,501 |
-30 - i*20 = -5 + 25 (-1) - i*20
|
983 |
Z = Q - Y \Rightarrow Q = Z + Y
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27,209 |
\cos\left(\sin^{-1}{-y}\right) = \cos(-\sin^{-1}{y}) = \cos\left(\sin^{-1}{y}\right)
|
-486 |
e^{19 \frac{i\pi}{6}11} = (e^{\frac{i\pi}{6}11})^{19}
|
27,098 |
\cos(\pi/2) = \cos(\frac32 \cdot \pi) = 0
|
1,050 |
z \cdot 21/20 = 4 \cdot z/5 + z/4
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-5,464 |
\frac{l\cdot 3}{25\cdot \left(-1\right) + l^2} = \frac{l\cdot 3}{(5 + l)\cdot (5\cdot (-1) + l)}
|
15,859 |
\cot(-B) = z \Rightarrow \operatorname{arccot}(z) = -B
|
13,534 |
\frac12\sin{y \cdot 2} = \cos{y} \sin{y}
|
-90 |
-13 + 2\cdot (-1) = -15
|
8,008 |
\frac{3 + n}{(-1) + n} = 1 + \frac{4}{n + (-1)}
|
12,180 |
0 = 315 \cdot (-1) - 3 \cdot b \cdot b + 66 \cdot b rightarrow b^2 - 22 \cdot b + 105 = (b + 15 \cdot (-1)) \cdot (b + 7 \cdot (-1)) = 0
|
8,186 |
80/10 \cdot 5 = 8 \cdot 5 = 40
|
5,211 |
(j + 1)/j = 1 + \tfrac1j
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25,363 |
\sqrt{X\cdot 4}/2 = \sqrt{X}
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32,158 |
i! = \dfrac{(i!)!}{(i! + (-1))!}
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42,230 |
2 + 67 + 22*(-1) + 6*\left(-1\right) = 41
|
22,153 |
\tfrac{1}{(1 - y)^3} = (1 + y + y^2 + \dots)^3
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-5,367 |
10^4*0.24 = 10^{(-5) (-1) - 1}*0.24
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20,536 |
\frac{1}{2} + \dfrac{1}{4} + 1/8 + \frac{1}{12} + 1/24 = 1
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-2,701 |
16^{1/2}*3^{1/2} - 3^{1/2}*9^{1/2} = 3^{1/2}*4 - 3*3^{1/2}
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-18,506 |
5*c + 10 = 6*\left(2*c + 2\right) = 12*c + 12
|
-12,496 |
3 = \frac{19.5}{6.5}
|
10,540 |
e^c\cdot e^d = e^{c + d}
|
-3,409 |
11^{1/2} \cdot 2 = 11^{1/2} \cdot (5 + 4 \cdot \left(-1\right) + 1)
|
5,289 |
\sigma(BA) \backslash 0 = \sigma\left(BA\right) \backslash 0
|
6,821 |
-\frac{9}{25} + 16/25 + \dfrac{12}{25} = 19/25
|
11,599 |
3 \cdot 5 + 2 \cdot 2 + 2 \cdot 4 + 2 \cdot 6 = -5 \cdot 3 + (2 + 5) \cdot 2 + 2 \cdot (6 + 5) + (4 + 5) \cdot 2
|
48,656 |
108\cdot (-1) + 120 = 12
|
7,621 |
h + z \cdot (1 + k) = y rightarrow \frac{-h + y}{1 + k} = z
|
26,780 |
\left(1 + x^4 + x^3 + x^2 + x\right)\cdot (\left(-1\right) + x) = x^5 + (-1)
|
14,137 |
1 + t^4 + t^2 = (t \cdot t + 1)^2 - t^2
|
40,161 |
3 \cdot 3 \cdot 4 = 36
|
-20,869 |
\frac{1}{z \cdot (-60)} \cdot (100 \cdot \left(-1\right) + 10 \cdot z) = \frac{1}{\left(-6\right) \cdot z} \cdot (z + 10 \cdot (-1)) \cdot 10/10
|
-20,817 |
\frac{1}{-24} \times (-n \times 9 + 21 \times (-1)) = (-n \times 3 + 7 \times (-1))/(-8) \times \dfrac33
|
-4,052 |
\frac{m}{40*m}*100 = 100/40*\dfrac{m}{m}
|
1,527 |
2\cdot k = m \implies (-1) + m\cdot 3 = (-1) + k\cdot 6
|
-23,571 |
12/25 = \frac{3}{5} \cdot \frac45
|
-4,939 |
7.4 \cdot 10^0 = 7.4 \cdot 10^{1 - 1}
|
10,916 |
1989/867 = \dfrac{51 \cdot 39}{51 \cdot 17} = 39/17
|
8,397 |
1 = \tfrac12*(3 + (-1))
|
8,418 |
36*3^{1/2} = 72*3^{1/2}/2
|
-9,158 |
49\cdot (-1) - 7\cdot k = -7\cdot 7 - 7\cdot k
|
-29,935 |
\frac{d}{dx} (-x^3) = -\frac{d}{dx} x \cdot x^2 = -3 \cdot x^2 = -3 \cdot x \cdot x
|
26,118 |
(\left(-1\right) + 1)*20 + 250 = 250
|
27,569 |
h \cdot b \cdot d = h \cdot b \cdot d = \frac{1}{b \cdot d} \cdot h
|
35,082 |
\frac{1}{1 - x^2} = (\frac{1}{1 - x} + \dfrac{1}{x + 1})/2
|
-5,081 |
10^{11}*48.0 = 48.0*10^{6 + 5}
|
31,515 |
-\dfrac{u}{u * u + 1} + u = \frac{1}{u * u + 1}*u * u * u
|
213 |
1 + 2*u = -u^2 + (u + 1)^2
|
1,862 |
(-1) + m \leq -r + x \Rightarrow 1 + x \geq m + r
|
-22,378 |
(n + 10)\cdot (n + 3\cdot (-1)) = n^2 + 7\cdot n + 30\cdot (-1)
|
27,729 |
a^2 \cdot a + b^3 = \left(a^2 - ab + b^2\right) (a + b)
|
-20,422 |
\frac{x \cdot 70 + 14 \cdot (-1)}{14 + x \cdot 35} = \frac{1}{7} \cdot 7 \cdot \dfrac{1}{2 + 5 \cdot x} \cdot (2 \cdot (-1) + 10 \cdot x)
|
-4,146 |
8m^2 = 8m^2
|
27,861 |
1/a = \tfrac1a
|
14,592 |
1/2\cdot 1/2\cdot \dfrac{1}{2} = 1/8
|
19,931 |
3^{2*x + 2} + (-1) = 3^{2*x}*3^2 + (-1) = 9*3^{2*x} + (-1) = 8*3^{2*x} + 3^{2*x} + (-1)
|
40,937 |
26^6 + 140552 (-1) = 308775224
|
20,600 |
m^2 + 2\cdot m + 1 = (m + 1)^2
|
9,015 |
\tfrac{0}{(0 + 2 \cdot \left(-1\right)) \cdot (0 + 1)} = \frac{0}{\left(-2\right)} = 0/2 = 0
|
10,550 |
2^k\cdot k + 2^{1 + k} = 2^{1 + k}\cdot (k + 1) - k\cdot 2^k
|
-8,387 |
\left(-6\right)*(-2) = 12
|
35,995 |
-2\times x \times x + 2\times (x^2 + x)^2 - 2\times x^4 = 4\times x^3
|
-26,673 |
8*z^2 - z*18 + 5*(-1) = \left(4*z + 1\right)*(5*(-1) + 2*z)
|
26,832 |
2^{15} + \left(-1\right) = \frac{1}{((-1) + 2 \cdot 2 \cdot 2) \cdot (\left(-1\right) + 2^5)} \cdot (2^{15} + (-1)) \cdot ((-1) + 2^5) \cdot (\left(-1\right) + 2^3)
|
2,540 |
AA^U = A^U A
|
28,190 |
x^2 - a^2 = \left(x - a\right) \cdot \left(a + x\right)
|
4,867 |
19 + s^4 - 20 \cdot s^2 = (s^2 + 19 \cdot \left(-1\right)) \cdot \left(s \cdot s + (-1)\right)
|
31,392 |
z^4 + 2*z + 1 = z^4 + 1 = (z + 1)^4
|
29,521 |
4\cdot a = \left(a + 1 + \rho\right)^2 = a^2 + 2\cdot \left(1 + \rho\right)\cdot a + (1 + \rho)^2
|
44,378 |
x = \dfrac{x}{1}
|
19,041 |
{l + (-1) + x - l + 1 + (-1) \choose l + (-1)} = {(-1) + x \choose l + (-1)}
|
1,351 |
(D - x) \cdot B \cdot D = B \cdot D \cdot \left(-x + D\right)
|
-20,396 |
-\frac{1}{4} \cdot \frac{1}{4 \cdot (-1) - r \cdot 5} \cdot \left(4 \cdot \left(-1\right) - r \cdot 5\right) = \dfrac{5 \cdot r + 4}{-r \cdot 20 + 16 \cdot (-1)}
|
-12,617 |
141*\left(-1\right) + 172 = 31
|
-20,235 |
\frac{x \cdot 90 + 50}{-20 \cdot x + 40 \cdot \left(-1\right)} = \frac{1}{10} \cdot 10 \cdot \frac{5 + x \cdot 9}{4 \cdot (-1) - x \cdot 2}
|
3,200 |
0 = 3\cdot \left(-1\right) + z^2\cdot 3\Longrightarrow 1 = z^2
|
1,817 |
\frac{2^4}{3^4} = 16/81
|
-24,251 |
7*10 + 7*\frac22 = 7*10 + 7 = 70 + 7 = 70 + 7 = 77
|
-27,626 |
-1 + 3 \cdot \left(-1\right) + 9 + 5 \cdot \left(-1\right) = -4 + 9 + 5 \cdot (-1) = 5 + 5 \cdot (-1) = 0
|
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