id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
30,906 |
l = (-1) + l \times 2 \Rightarrow 1 = l
|
-20,634 |
\dfrac{\left(-1\right)*5 n}{\left(-5\right) n}*3/8 = (\left(-1\right)*15 n)/(n*(-40))
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25,790 |
6 + 1^3 - 1^2 \cdot 2 - 5 = 0
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-22,991 |
\frac{3 \cdot 11}{4 \cdot 11} = 33/44
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9,048 |
( \alpha, y, z) + ( 2, 1, -5) = ( 5, 9, 0) rightarrow ( 5, 9, 0) = \left( 2 + \alpha, 1 + y, z + 5\left(-1\right)\right)
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-24,883 |
\frac{11}{12} = \frac{s}{12 \pi}\cdot 12 \pi = s
|
16,048 |
6 = a^3 + b^3 = a * a * a - (-b) * (-b) * (-b)
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18,363 |
2 - e = 0 \Rightarrow e = 2
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24,101 |
(q + 1)! - q! = (q + 1)\cdot q! - q! = (q + 1 + \left(-1\right))\cdot q! = q\cdot q!
|
-15,125 |
\dfrac{m^5}{\frac{1}{m^{10}} \frac{1}{z^6}} = \dfrac{1}{\frac{1}{m^{10} z^6}}m^5
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-18,366 |
\dfrac{z^2 - z - 12}{z^2 - 9} = \dfrac{(z - 4)(z + 3)}{(z - 3)(z + 3)}
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-15,225 |
\frac{x^{15}}{x^4\cdot l^4} = \tfrac{x^{15}\cdot \frac{1}{x^4}}{l^4} = \dfrac{1}{l^4}\cdot x^{15 + 4\cdot (-1)} = \frac{x^{11}}{l^4}
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34,335 |
\frac{4896}{3\cdot 2}1 = 816
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-26,187 |
\tfrac{1}{3} 15 = 5
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-1,129 |
\frac{(-1) \frac{1}{2}}{\frac18} = 8/1 \left(-1/2\right)
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31,087 |
\frac{1}{4}*(87^{1 / 2} - 9) = 87^{\frac{1}{2}}/4 - 9/4
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-8,086 |
\tfrac{i\cdot 7 + 3}{-i - 1} = \frac{1}{-1 - i}(i\cdot 7 + 3) \frac{1}{-1 + i}(i - 1)
|
7,992 |
p_2 \cdot p_1 + y^2 - (p_1 + p_2) \cdot y = \left(-p_1 + y\right) \cdot (y - p_2)
|
9,099 |
\cos{q}\cdot \sin{q} = \dfrac12\cdot \sin{2\cdot q}
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-9,176 |
-12 \cdot n + 12 \cdot (-1) = -3 \cdot 2 \cdot 2 - 2 \cdot 2 \cdot 3 \cdot n
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25,736 |
\frac{z^9 + y^9}{z^9\cdot y^9} = \frac{1}{y^9} + \frac{1}{z^9}
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19,730 |
1 + x/1 + \frac{1}{2!}x * x + x^3/3! + x^4/4! + ... + (-1) = e^x + (-1)
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41,810 |
2\arctan\frac{\sqrt{3^2+(-4)^2+(-1)^2}}{\sqrt{2^2+3^2+(-6)^2}}=2\arctan\frac{\sqrt{26}}{7}
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21,750 |
x \cdot x + (-1) = (1 + x) ((-1) + x)
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41,874 |
9 = 3 + 2\cdot 3
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9,134 |
Q = (8 \cdot Q^2)^{1/2}/3 = \dfrac{1}{3} \cdot 2 \cdot Q \cdot 2^{1/2}
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7,459 |
2*\pi = \pi*2/5*2 + 3*\dfrac{2*\pi}{5}
|
14,062 |
\Delta F x = Fx\Delta
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-6,424 |
\frac{4}{h \cdot 3 + 27 \cdot \left(-1\right)} = \frac{4}{3 \cdot (h + 9 \cdot (-1))}
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-3,517 |
0.2 = \frac{1}{10}\cdot 2
|
14,829 |
2^np^n = (2p)^n
|
-19,001 |
2/5 = C_r/\left(4*\pi\right)*4*\pi = C_r
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-20,474 |
\left(6 + r\right) \cdot \frac{1}{r + 6}/8 = \frac{6 + r}{r \cdot 8 + 48}
|
-22,800 |
24/32 = \frac{3}{8\cdot 4}\cdot 8
|
12,242 |
\cot\left(y\right) = \tan(\frac{\pi}{2} - y)
|
20,819 |
4^2 - 3\cdot 4 + 2\cdot \left(-1\right) = 2 = \sqrt{4}
|
14,455 |
(C + D) (X_1 + X_2) = D*(X_1 + X_2) + \left(X_2 + X_1\right) C
|
34,645 |
0.3^2=0.09
|
-20,094 |
\frac{1}{15 q} (15 q + 10 (-1)) = \frac{2 \left(-1\right) + q*3}{3 q}*5/5
|
10,908 |
\pi/4 + \frac{\pi}{12} = \dfrac{\pi}{3}
|
-20,733 |
(6 t + 36 (-1))/48 = \frac{6}{6} (t + 6 \left(-1\right))/8
|
4,913 |
s = r^{a \cdot m} \cdot s^{b \cdot m} = (r^a \cdot s^b)^m
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-27,438 |
(c^2 - 10 c + 25) c^2 = c^4 - 10 c^3 + 25 c^2
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-20,433 |
-\frac61 \dfrac{3i + 8}{i*3 + 8} = \frac{1}{8 + 3i}(-18 i + 48 \left(-1\right))
|
10,725 |
x^2 \times 2 - 6 \times x + 8 \times (-1) = 2 \times (x + 1) \times (x + 4 \times (-1))
|
-20,323 |
4/4 \frac{1}{-10}(2y + 2) = \tfrac{1}{-40}(y\cdot 8 + 8)
|
4,678 |
2\cdot z \cdot z + j\cdot z\cdot 2 + j \cdot j = z \cdot z + (z + j) \cdot (z + j)
|
-7,263 |
\dfrac{6}{14} \cdot \dfrac{4}{13} = \dfrac{12}{91}
|
951 |
\epsilon/2 + \frac{1}{2}*\epsilon = \epsilon
|
13,795 |
\frac{1}{I + L} = I - L + L^2 - L^2 * L + ...
|
-5,535 |
\dfrac{4}{3\cdot (2\cdot \left(-1\right) + x)} = \frac{4}{6\cdot \left(-1\right) + x\cdot 3}
|
-9,868 |
0.01\cdot (-70) = -\dfrac{70}{100} = -\frac{1}{10}\cdot 7
|
12,046 |
\frac{76!}{76! - 75!} = \frac{76*75!}{75! \left(76 + (-1)\right)} = \frac{76}{75}
|
35,734 |
23382^2 - 13 \times 6485^2 = -1
|
26,589 |
78 = 13\cdot (2\cdot (-1) + 13 + 1)/2
|
27,114 |
2 \cdot (-1) + i + 2 = i
|
-4,674 |
\frac{6\cdot (-1) + 2\cdot z}{3\cdot (-1) + z^2 + z\cdot 2} = -\frac{1}{(-1) + z} + \frac{3}{3 + z}
|
21,185 |
-\tfrac{3 \cdot x + 4 \cdot y}{5 \cdot \epsilon - 8 \cdot u} = -\frac{1}{(5 \cdot \epsilon - 8 \cdot u) \cdot (-1)} \cdot (-3 \cdot x + 4 \cdot y) = \frac{1}{8 \cdot u - 5 \cdot \epsilon} \cdot (3 \cdot x + 4 \cdot y)
|
-21,038 |
-\frac{8}{56} = \tfrac{1}{8}\times 8\times \left(-\frac17\right)
|
10,472 |
1/4 = \tfrac{2}{3}*\dfrac{3}{8}
|
24,042 |
(2^{1/9})^3 = 2^{\dfrac13}
|
-16,588 |
18^{1/2}\cdot 10 = (9\cdot 2)^{1/2}\cdot 10
|
-1,922 |
π*19/12 + \frac{π}{2} = 25/12*π
|
-11,528 |
-37 - 5\cdot i = -12 + 25\cdot (-1) - i\cdot 5
|
-24,179 |
(6 + 4)^2 = 10 \cdot 10 = 10^2 = 100
|
12,392 |
\frac12*8^{\frac{1}{2}} = 2^{1 / 2}
|
25,657 |
2 + 5\left(-1\right) + 4\left(-1\right) + 3(-1) = -10
|
-22,313 |
72 + r \cdot r + r \cdot 17 = (r + 8) \cdot \left(9 + r\right)
|
-10,052 |
-\dfrac{1}{20} 17 = -0.85
|
46,315 |
24+36+32+8=100
|
25,720 |
\left(z \cdot 9 = 1000 \cdot L + z \implies z \cdot 8 = L \cdot 1000\right) \implies z = 125 \cdot L
|
25,412 |
ghg/g = gh
|
35,644 |
\sin\left(x + \pi\right) = \sin(-x)
|
6,644 |
\binom{n + (-1)}{k} + \binom{(-1) + n}{k + (-1)} = \binom{n}{k}
|
23,064 |
147456 = 2^{14} \cdot 3^2
|
-10,621 |
-\tfrac{67}{50} = -67/50
|
5,313 |
7/6 = \dfrac{1}{2} + \tfrac{1}{3} + \tfrac{1}{3}
|
27,952 |
\frac1db = b/d
|
39,479 |
-\frac23 = -\frac132
|
-20,805 |
\frac{q \cdot 6 + 5}{6 \cdot q + 5} \cdot (-4/1) = \frac{1}{6 \cdot q + 5} \cdot (-24 \cdot q + 20 \cdot (-1))
|
-2,450 |
\sqrt{250} + \sqrt{10} = \sqrt{10} + \sqrt{25 \cdot 10}
|
15,460 |
\int_y^1 ...\,dy = -\int\limits_1^y ...\,dy
|
25,643 |
x \cdot 5 + 4 \cdot (-1) - x \cdot 3 + 1 = x \cdot 2 + 5 \cdot \left(-1\right)
|
-23,246 |
1/9 \cdot 4/2 = 2/9
|
39,950 |
7^2 \cdot 7 = 7^2 \cdot 7
|
31,260 |
Bx = \begin{pmatrix}1 & -1\\0 & 1\end{pmatrix} = \frac{1}{xB}
|
-1,625 |
\frac{3}{2}\pi + 0 = \frac{3}{2}\pi
|
2,793 |
H/a = H*H/a = x*H*\frac{H}{a} = x*H/a
|
30,038 |
A\cdot (y + x) = x\cdot A + y\cdot A
|
2,272 |
-s + s_x < \epsilon \Rightarrow s_x < s + \epsilon
|
7,743 |
\frac{\mathrm{d}}{\mathrm{d}x} (x^3 + 2\cdot x \cdot x + x\cdot 3 + 4) = x \cdot x\cdot 3 + x\cdot 4 + 3
|
9,797 |
\sin(v) = \sin\left(w\right) \Rightarrow w = v
|
23,577 |
6^m = (5 + 1)^m
|
23,281 |
-614/3299 = -\frac{1}{3299}614
|
37,525 |
1 = 1 \cdot \dotsm
|
-2,949 |
11^{1 / 2}*\left(2 + 3 + (-1)\right) = 4*11^{\dfrac{1}{2}}
|
-29,349 |
(g + b) (g - b) = g^2 - b^2
|
2,256 |
\mathbb{N} = \left\{\ldots, 2, 3, 1, 0, 4\right\}
|
7,531 |
(x + a) \cdot \left(b + x\right) = a \cdot b + x^2 + x \cdot \left(a + b\right)
|
27,383 |
\left(-1\right) + d^l = \left(d + 1\right)*(d^{l + \left(-1\right)} - d^{2*(-1) + l} + d^{3*(-1) + l} - \cdots + d + (-1))
|
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