id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-4,396 |
\dfrac{4}{7} \cdot p^3 = 4/7 \cdot p^3
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-5,572 |
\frac{z}{(z + 6)\cdot \left(z + 1\right)}\cdot 3 = \frac{z\cdot 3}{6 + z^2 + 7\cdot z}
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-16,524 |
7 \cdot \sqrt{25} \cdot \sqrt{11} = 7 \cdot 5 \cdot \sqrt{11} = 35 \cdot \sqrt{11}
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17,791 |
\frac17\cdot 390 = 10\cdot 39/7
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10,404 |
(\left(1 + 5^{1/2}\right)/2)^2 = (3 + 5^{1/2})/2
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37,692 |
\cos(2u) = -2\sin^2(u) + 1
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-12,008 |
\tfrac19 = \frac{1}{12 \cdot \pi} \cdot s \cdot 12 \cdot \pi = s
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-2,341 |
\frac{7}{16} = \frac{8}{16} - \frac{1}{16}
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22,071 |
10/60 = 1/6
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-4,576 |
z^2 + 5\cdot z + 6 = (3 + z)\cdot (2 + z)
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-10,398 |
-8 = 5*y + 9*(-1) + 10*(-1) = 5*y + 19*\left(-1\right)
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11,932 |
f \cdot b = \|f\| \cdot \|b\| \cdot (\cos(x) + i \cdot \sin(x)) = \|f\| \cdot \|b\| \cdot e^{i \cdot x}
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1,431 |
\frac{1}{(-1) + l^2}\times 2 = \dfrac{1}{(-1) + l} - \frac{1}{l + 1}
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52,928 |
\cos{-\chi} = \cos{\chi}
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31,778 |
17! = 17\times 16\times 15\times \dotsm\times 2
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-20,007 |
\frac{4}{9} \frac{7 - 4p}{-p*4 + 7} = \frac{-16 p + 28}{-36 p + 63}
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35,403 |
\frac{1}{2 \cdot (-1) + x} \cdot (2 \cdot (-1) + x) \cdot (2 \cdot (-1) + x) = 2 \cdot (-1) + x
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4,790 |
1/C = (1/C)^Z = \frac{1}{C^Z}
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27,831 |
1.96\cdot (1/(4\cdot l))^{1/2} = \frac{1}{2\cdot l^{1/2}}\cdot 1.96 \approx \dfrac{1}{l^{1/2}}
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10,988 |
3 = c + 2 \cdot (-1) \Rightarrow c = 5
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5,558 |
(4 + \text{i})\cdot (4 - \text{i}) = 17
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2,863 |
\frac{1}{c\cdot 1/g} = g/c
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15,955 |
\frac{1}{405} = 4\cdot \frac{1}{9}/180
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34,035 |
3 \cdot x_3 \cdot x_2 \cdot x_1 = x_2 \cdot x_1 \cdot x_3 + x_2 \cdot x_3 \cdot x_1 + x_2 \cdot x_1 \cdot x_3
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-3,116 |
\left(5 + 4 + 2\cdot (-1)\right)\cdot 3^{\frac{1}{2}} = 3^{\frac{1}{2}}\cdot 7
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-2,880 |
-5^{1/2} + (4 \cdot 5)^{1/2} = 20^{1/2} - 5^{1/2}
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5,547 |
-(k + 2) \cdot (k + 2) + \left(k + 3\right)^2 = 2k + 5
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6,994 |
-16 = 4\cdot d \implies d = -4
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3,103 |
\frac{1}{z_1*z_2} = 1/(z_2*z_1) = z_2*z_1 = z_1*z_2
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3,462 |
r = r - f r + f r = (1 - f) r + f r
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210 |
(z^2 - 2*z*y + y^2)^{\frac{1}{2}} = \left((z - y)^2\right)^{1 / 2} = |z - y|
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23,079 |
6000 = 5^2 * 5*4 * 4*3
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-7,279 |
\frac{1}{28} \cdot 9 = \frac{3}{4} \cdot 3/7
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23,955 |
3/2 - -\dfrac{1}{2}\cdot 5 = 4
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1,356 |
\dfrac{1}{q + (-1)} \cdot \left(q^7 + (-1)\right) = 1 + q^6 + q^5 + q^4 + q^3 + q^2 + q
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18,290 |
(7500 - 60*20 - 80*60)/30 = 1500/30 = 50
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10,657 |
-z*x + 0 = x*z + z*(-x) - z*x
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-4,299 |
\dfrac{x^4}{x^4}*55/40 = \frac{1}{40 x^4} x^4*55
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45,348 |
\tanh x=\frac{e^{2x}-1}{e^{2x}+1} \Rightarrow \tanh \frac{x}{2}=\frac{e^{x}-1}{e^{x}+1}
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42,448 |
\frac{1}{36} = \frac{1}{6\cdot 6}
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-4,732 |
(x + 1)\cdot \left(2 + x\right) = x \cdot x + x\cdot 3 + 2
|
-491 |
\frac{7}{6}\cdot \pi = -\pi\cdot 8 + \frac{55}{6}\cdot \pi
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32,042 |
\frac{7!\cdot 30}{9!} = 5/12
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-717 |
\pi \cdot \frac{17}{3} - 4 \cdot \pi = \frac13 \cdot 5 \cdot \pi
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14,161 |
-y^2\cdot 2 + 4\cdot y + 6 = 5\cdot (-1) + y + 11 - 2\cdot y \cdot y + 3\cdot y
|
72 |
x^3 = y * y^2 = z^3 = x*y*z
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8,254 |
2\cdot 3 = -((-6)^{\frac{1}{2}})^2 = 6
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-16,574 |
8 \cdot 25^{1 / 2} \cdot 2^{1 / 2} = 8 \cdot 5 \cdot 2^{1 / 2} = 40 \cdot 2^{1 / 2}
|
7,865 |
\sin^2{f_1} - \cos^2{f_2} = 1 - \cos^2{f_1} - \cos^2{f_2} = \sin^2{f_2} - \cos^2{f_1}
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16,051 |
-(x^2 x + 1) + 3 = -x^3 + 2
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28,901 |
2\cdot (5^2 + 5^2) = 6^2 + 8^2
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22,318 |
4 \cdot (-1) + a^3 - 3 \cdot a^2 + 5 \cdot a = \left(a + \left(-1\right)\right)^3 + 2 \cdot ((-1) + a) + (-1)
|
8,132 |
\cos^2{z} = \left(1 + \cos{2\cdot z}\right)/2
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-2,303 |
2/18 = \frac{1}{18}\cdot 4 - 2/18
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35,210 |
1 = x - j \Rightarrow (-1) + x = j
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22,609 |
\cos(x) = \cos(\pi\cdot 2 + x)
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-12,153 |
17/40 = s/\left(16 \pi\right)*16 \pi = s
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18,642 |
\mathbb{E}\left[T\right]^{-1} = \mathbb{E}\left[\dfrac1T\right]
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-18,967 |
\frac{1}{15}\cdot 2 = \frac{1}{9\cdot \pi}\cdot A_x\cdot 9\cdot \pi = A_x
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25,470 |
\left(x\cdot 2 - 3\cdot y - 3\cdot y'\cdot x + y'\cdot y\cdot 2 = 0\Longrightarrow y'\cdot (y\cdot 2 - 3\cdot x) = -2\cdot x + 3\cdot y\right)\Longrightarrow \frac{3\cdot y - 2\cdot x}{-3\cdot x + y\cdot 2} = y'
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-23,161 |
-\frac{32}{27} = -16/9 \cdot \dfrac{1}{3} \cdot 2
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-2,227 |
9/13 - 5/13 = \dfrac{4}{13}
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-3,806 |
q \cdot q \cdot \frac{8}{5} = \frac15 \cdot 8 \cdot q^2
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46,379 |
3! \cdot 2 \cdot 2 \cdot 2 = 48
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10,856 |
-g = g + f + ef = gf + fe + eg - e = gfe
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22,459 |
2^{2\cdot q} + 2^{2\cdot q + 3} = (3\cdot 2^q) \cdot (3\cdot 2^q)
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-9,149 |
-m*3*3*7 + 7 = -m*63 + 7
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-18,457 |
3 \times d + 10 \times (-1) = 9 \times (d + 5 \times \left(-1\right)) = 9 \times d + 45 \times (-1)
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-12,531 |
8 = \dfrac{1}{11.5}\cdot 92
|
9,250 |
\frac{1}{z\cdot 1/y} = y/z
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-20,641 |
\frac{1}{-6*t + 15*(-1)}*(24*(-1) - 9*t) = 3/3*\frac{1}{-2*t + 5*\left(-1\right)}*(-3*t + 8*(-1))
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15,153 |
(1 + 4 \cdot d^2)^{1/2} < (1 + 4 \cdot d + 4 \cdot d^2)^{1/2} = ((1 + 2 \cdot d) \cdot (1 + 2 \cdot d))^{1/2} = 1 + 2 \cdot d
|
24,593 |
\left(x + 3\left(-1\right)\right) (x + 6\left(-1\right)) = 18 + x^2 - 9x
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-3,578 |
\frac{r^5}{r} = \frac{1}{r} \cdot r^5 = r^4
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34,035 |
x_3 \cdot x_2 \cdot x_1 + x_3 \cdot x_1 \cdot x_2 + x_2 \cdot x_1 \cdot x_3 = x_3 \cdot x_2 \cdot x_1 \cdot 3
|
6,201 |
-(a \cdot a^2 - a) = (-a)^2 \cdot (-a) - -a
|
14,249 |
71 = 7 \cdot a + 13 \cdot (-1) \implies a = 12
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37,650 |
24 = 2*2*6
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-7,602 |
\dfrac{11 + i\cdot 16}{-5\cdot i + 2} = \frac{2 + i\cdot 5}{2 + i\cdot 5}\cdot \dfrac{16\cdot i + 11}{-5\cdot i + 2}
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5,783 |
-(k + \left(-1\right))^2 = -k^2 + k\cdot 4 + (-1) - 2\cdot k
|
-20,909 |
\tfrac{1}{7\cdot l + 28\cdot \left(-1\right)}\cdot \left(l + 4\cdot \left(-1\right)\right) = \dfrac{1}{7}\cdot 1
|
-24,663 |
3/\left(3*4\right) = 3/12
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-3,740 |
\frac{8*3}{3*5}*\frac{p^3}{p^2} = 24/15*\frac{p^3}{p^2}
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21,890 |
\frac{1}{a*b} = 1/(a*b) = \frac{1}{a*b} = \frac{1}{a*b}
|
9,963 |
(1 + 4)\cdot 5^{n + 1} = 5^{n + 1} + 4\cdot 5^{1 + n}
|
16,618 |
b\cdot a\cdot 2 = b\cdot a + b\cdot a
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1,665 |
1 - \frac{1}{2^l} = \frac{1}{2^l}\cdot (2^l + \left(-1\right))
|
7,796 |
A^3 - 3A + 2(-1) = (1 + A)^2 (A + 2(-1))
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-21,036 |
8/8*\left(-7/9\right) = -56/72
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25,984 |
{6 \choose 3} + 7 \cdot 7 \cdot 6 + {7 \choose 3} \cdot 2 = 384
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-20,028 |
\frac{1}{8 \cdot (-1) + q \cdot 8} \cdot \left(q + 6 \cdot \left(-1\right)\right) \cdot \frac{6}{6} = \frac{q \cdot 6 + 36 \cdot (-1)}{q \cdot 48 + 48 \cdot (-1)}
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-20,980 |
\tfrac{r + 10}{r + 10}\cdot \left(-9/10\right) = \frac{1}{r\cdot 10 + 100}\cdot (-9\cdot r + 90\cdot (-1))
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5,712 |
\left(-3*x + 4 = z\Longrightarrow 4*(-1) + z = -x*3\right)\Longrightarrow \frac{1}{-3}*\left(4*\left(-1\right) + z\right) = x
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-20,347 |
(16\cdot (-1) - 40\cdot k)/(-80) = \left(-5\cdot k + 2\cdot (-1)\right)/(-10)\cdot 8/8
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33,466 |
\dfrac{1}{k!} k k = \dfrac{1}{(2 \left(-1\right) + k)!} + \tfrac{1}{(k + (-1))!}
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-20,056 |
\frac{k \cdot 5 + 1}{k \cdot \left(-9\right)} \cdot 9/9 = \frac{45 \cdot k + 9}{(-81) \cdot k}
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23,172 |
(2^2 - 1^2) * (2^2 - 1^2) + (2*2) * (2*2) = \left(1^2 + 2^2\right) * \left(1^2 + 2^2\right)
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9,830 |
(P(X) + P(B)) * (P(X) + P(B)) = P(X) * P(X) + 2*P(X)*P(B) + P(B) * P(B) = 1 \Rightarrow 0.9 = P(B) * P(B) + P(X)^2
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25,199 |
2^{20} + (-1) = (2^{10} + (-1))*(2^{10} + 1) = (2^5 + (-1))*(2^5 + 1)*(2^{10} + 1)
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-18,441 |
\frac{1}{s^2 - s \cdot 11 + 30} (-s \cdot 5 + s^2) = \dfrac{(s + 5 (-1)) s}{\left(5 \left(-1\right) + s\right) (6 (-1) + s)}
|
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