id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
15,604 |
x\cdot y' + y = x - y\cdot y'
|
-2,387 |
(-9)^3 = \left(-9\right)*(-9)*\left(-9\right) = 81*(-9) = -729
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26,221 |
z/y\cdot a = \frac{a}{y}\cdot z
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48,276 |
98! = 98!
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11,243 |
5^2 + 5^2 = 1^2 + 7 * 7 = 50
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-4,541 |
\frac{5\cdot (-1) - z}{\left(-1\right) + z \cdot z} = \frac{1}{1 + z}\cdot 2 - \frac{3}{z + (-1)}
|
25,338 |
2 \cdot 2 + 3^2 + 6^2 = 7^2
|
17,829 |
[\frac{n}{2}]=[\frac{n}{4}]+[\frac{\frac{n}{2}+1}{2}]=[\frac{n}{4}]+[\frac{n+2}{4}]
|
17,511 |
\frac{1}{4^n} = \frac{1}{\left(2^n\right)^2}
|
30,955 |
\sqrt{1 - \sin(2 \cdot y)} = \sqrt{(\sin(y) - \cos(y)) \cdot (\sin(y) - \cos(y))} = \sqrt{\left(\cos(y) - \sin(y)\right)^2}
|
-20,240 |
\frac{49*(-1) + 35*z}{7 - z*5} = -7/1*\frac{1}{-5*z + 7}*\left(7 - 5*z\right)
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-8,138 |
10 = 5\cdot 2
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10,179 |
\frac{1}{3^l \dfrac{1}{5^l}} = \left(5/3\right)^l
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32,487 |
\binom{7}{2}*5 = 7!/(1!*4!*2!)
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-10,831 |
13 = \tfrac{156}{12}
|
31,399 |
\cos{y} = \sin\left(\dfrac{\pi}{2} - y\right)
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41,039 |
(2 + 3)^2 = 2 \cdot 2 + 2 \cdot 2 \cdot 3 + 3^2 = 4 + 12 + 9 = 25
|
3,585 |
(m + 1)/2\cdot 2 = 1 + m
|
22,640 |
\cos(|z y|) = \cos{-z y} = \cos{z y}
|
14,743 |
-((-1) + k)*\left(1 + k\right) + k*x = \left(k + 1 + (-1)\right)*x - \left(k + 1 + 2*(-1)\right)*(k + 1)
|
-2,218 |
\frac{4}{19} = -3/19 + 7/19
|
16,687 |
x^1*x^{1/2} = x*x^{1/2}
|
5,944 |
(2\cdot m + x)^2 = x \cdot x + 4\cdot m \cdot m + m\cdot x\cdot 4
|
-27,491 |
a^2\cdot 8 = 2\cdot a\cdot a\cdot 2\cdot 2
|
-173 |
\frac{1}{(8 + 3 \left(-1\right))!} 8! = 8*7*6
|
17,543 |
D_x \cdot D_k \cdot D_i = D_k \cdot D_x \cdot D_i
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24,188 |
7/3 = \tfrac{7}{3}
|
5,468 |
1 + 3\cdot q^1 + 5\cdot q^2 + \dots = \frac{2\cdot q}{(q + (-1))^2} - \frac{1}{q + (-1)} = \frac{q + 1}{(q + (-1))^2}
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29,091 |
1/6 = 4\cdot \frac{1}{3}/8
|
26,118 |
250 = 250 + \left((-1) + 1\right)*20
|
13,522 |
x\cdot y = 0 \implies 0 = x\text{ or }0 = y
|
19,874 |
170 = \frac{5!}{2!\cdot 2!}\cdot 3 + 4\cdot 5!/(2!\cdot 3!) + 2\cdot 5!/3!
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29,826 |
\binom{2\cdot n}{n} = \frac{(2\cdot n)!}{n!^2} \approx 4^n/(\sqrt{\pi\cdot n})
|
715 |
-\tfrac{1}{m + 1} + \dfrac{2}{m + 2} = \frac{1}{\left(m + 2\right) (m + 1)}m
|
329 |
n^2 + \left(-1\right) = (n + (-1))\cdot (n + 1)
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26,473 |
|C \cup \left(A \cup E\right)| = |A \cup (C \cup E)| = |A| + |C \cup E| - |A \cap (C \cup E)|
|
-3,256 |
(2 + 4) \cdot \sqrt{3} = \sqrt{3} \cdot 6
|
15,104 |
π*2/3 = \tfrac23 π
|
13,624 |
2\cdot a = 2 - 2\cdot b \Rightarrow a = 1 - b
|
2,830 |
2 \times \left(-1\right) + 2 + c = c
|
12,979 |
1 + x + \left(-1\right) + p + (-1) = p + x + (-1)
|
-16,701 |
{5n} = ({5n} \times -3n) + ({5n} \times -1) = (-15n^{2}) + (-5n) = -15n^{2} - 5n
|
28,438 |
m*\left(1 + p\right) = k*\left(1 + p\right) \Rightarrow k + k p = p m + m
|
-26,406 |
\frac{1}{729*9^{12}} = 9^{-3 + 12*(-1)} = 1/205891132094649
|
22,251 |
z^5 + z + 1 = \left(z^2 + z + 1\right) \left(z^3 - z^2 + 1\right)
|
615 |
\dfrac{1}{p^2} \cdot \epsilon \cdot \beta \cdot 2 = \frac{\beta}{p} \cdot 2 \cdot \epsilon/p
|
8,379 |
\frac{9}{9}\cdot \frac{1}{10} = \frac{1}{10}
|
-890 |
\frac{3}{10000} + 0 + 6/10 + \frac{1}{100}\cdot 5 + \frac{0}{1000} = 6503/10000
|
23,117 |
\left(2\cdot n + 1\right)^2 + 2\cdot n + 1 + 1 = 4\cdot n^2 + 6\cdot n + 2 + 1 = 2\cdot (2\cdot n \cdot n + 3\cdot n + 1) + 1
|
19,591 |
(v + u) * (v + u) * (v + u) - u^3 - v^3 = 3(u + v) (-v) (-u)
|
4,588 |
\left(z + (-1)\right) \cdot (z^4 + z^3 + z^2 + z + 1) = z^5 + \left(-1\right)
|
-20,511 |
\frac{8}{8} \cdot \frac{7}{p + 10 \cdot \left(-1\right)} = \frac{1}{80 \cdot (-1) + p \cdot 8} \cdot 56
|
2,434 |
d^n \cdot d = d^{1 + n}
|
5,919 |
147 (-7) + 258\cdot 4 = 3
|
34,554 |
\frac12 \cdot (1 - 5^{1/2}) = 1/2 - \tfrac{5^{1/2}}{2}
|
829 |
0 = y \cdot y^2 + z^3 \Rightarrow 0 = (z + y)\cdot (z \cdot z - z\cdot y + y \cdot y)
|
11,712 |
6^{x + 1} + (-1) = 5 \cdot p + 5 \cdot 6^x = 5 \cdot (p + 6^x)
|
15,074 |
x - b = n*k\Longrightarrow x = b + k*n
|
21,952 |
\binom{(-1) + n + p}{p} = \dfrac{((-1) + n + p)!}{p! \left((-1) + n\right)!}
|
-7,488 |
\dfrac{30}{6} = 5
|
940 |
n\cdot 3 + 3\cdot \left(-1\right) = n + 2\cdot (-1) + n + n + (-1)
|
28,860 |
\frac{15 + 4(-1)}{2 + (-1)} = 11
|
23,578 |
a \cdot h \cdot g = a \cdot h/g = \frac{1}{h \cdot \frac1g} \cdot a = a \cdot g/h
|
12,551 |
\rho^5 + (-1) = (1 + \rho^4 + \rho^3 + \rho^2 + \rho) \cdot (\left(-1\right) + \rho)
|
856 |
d_1^6 = d_2 d_2 d_1^4 \Rightarrow d_1^4 = d_2 d_1^6 d_2 = d_1^9
|
15,237 |
\tan\left(\pi/2 - y\right) = \dfrac{1}{\sin{y}} \cdot \cos{y} = \frac{1}{\tan{y}}
|
11,738 |
\frac{1}{9} 4 = 4/6*4/6
|
-20,967 |
\frac{1}{(-12) \times t} \times \left(-42 \times t + 24\right) = \dfrac{6}{6} \times \frac{-7 \times t + 4}{\left(-2\right) \times t}
|
25,608 |
1 + y^6 = (1 + y^4 - y^2)\cdot (1 + y^2)
|
-19,469 |
\frac{1}{5}*2/(4*1/5) = \frac{2}{5}*\frac{5}{4}
|
-2,616 |
\sqrt{2}\cdot 7 = \sqrt{2}\cdot (4 + 3)
|
14,900 |
-\dfrac{2}{1 + t^2} + 1 = \dfrac{t^2 + (-1)}{t^2 + 1}
|
27,749 |
5 \left(-1\right) + z z^2 - z*7 = (4 (-1) + z) \left(z^2 + 4 z + 9\right) + 31
|
5,691 |
\frac{1}{15}\cdot \left(70\cdot \left(-1\right) + 75\right) = 1/3
|
18,306 |
\dfrac{1}{2} = \frac24 = 50/100
|
9,136 |
\frac{1}{2^{m + (-1)}} = \tfrac{1 \cdot 2}{2^{m + (-1)} \cdot 2} = \frac{2}{2^m}
|
-2,460 |
\sqrt{7} \cdot (2 \cdot (-1) + 4) = 2 \cdot \sqrt{7}
|
25,692 |
N - k + (-1) = N + 2*\left(-1\right) - k + (-1)
|
4,907 |
Z \cdot Z^{24} = Z^{25}
|
50,715 |
\left\{z\right\} = z^2 = z \cdot z \cdot z
|
-4,078 |
\frac{28*m^2}{36*m} = \tfrac{28}{36}*\frac{m^2}{m}
|
15,649 |
x + 2\left(a + (-1)\right) = 3a \Rightarrow x = a + 2
|
17,118 |
(1 + l) \left(l + (-1)\right) = l^2 + (-1)
|
27,727 |
{4 \choose 2}*{6 + 4 + (-1) \choose 6} = 504
|
5,620 |
b \cdot \gamma \cdot d = d \cdot b \cdot \gamma
|
10,486 |
1 = 2\cdot Z^3 + Z = Z\cdot (2\cdot Z^2 + 1) = (Z^3 + 1)\cdot \left(2\cdot Z^2 + 1\right)
|
13,364 |
48 = 1 + 50 + 3 \times (-1)
|
3,448 |
K_i^t\cdot A\cdot K_l = (A^t\cdot K_i)^t\cdot K_l = (A\cdot K_i)^t\cdot K_l
|
29,979 |
x^6 + x^4 + x^3*2 - x * x + x + 2*(-1) = x^6 + x^4 + x^3 - x^2 + (-1) + x^3 + x + (-1)
|
31,118 |
5 = 3M^2 + 2b^3 = 3M^2 + (-1) + 3b * b + 2b * b * b + 1 - 3b^2
|
24,026 |
\frac{1}{\sqrt{1 + \zeta^2} + \zeta} = -\zeta + \sqrt{\zeta^2 + 1}
|
-18,983 |
\frac{1}{6} = \frac{1}{4 \cdot \pi} \cdot X_r \cdot 4 \cdot \pi = X_r
|
-22,560 |
-\frac45\cdot \frac57 = (\left(-4\right)\cdot 5)/(5\cdot 7) = -\frac{20}{35} = -4/7
|
-5,521 |
\dfrac{2(q + 2)}{2(q + 7)(q + 2)} + \dfrac{2(q + 7)}{2(q + 7)(q + 2)} - \dfrac{6}{2(q + 7)(q + 2)} = \dfrac{ 2(q + 2) + 2(q + 7) - 6}{2(q + 7)(q + 2)}
|
-15,943 |
\frac{1}{10}2*6 - 8/10*6 = -36/10
|
23,526 |
1\cdot 2 \cdot 2 \cdot 2 + 2^2\cdot 0 + 1\cdot 2^1 + 2^0\cdot 0 = 10
|
7,638 |
\frac1t = \frac{4}{4 \cdot t}
|
45,262 |
22 = 3\cdot 7 + 1
|
-13,234 |
0.644 = \tfrac{1}{0.02} \cdot 0.01288
|
9,350 |
\frac{1}{2 \cdot 2} = 1/2 1/2 = 1/4
|
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