id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
9,820 |
\frac{1}{y^2} + y \cdot y = 2 \cdot (-1) + \left(y + \dfrac{1}{y}\right)^2
|
-6,100 |
\tfrac{3 \cdot r}{r^2 + r \cdot 18 + 80} = \dfrac{1}{(r + 8) \cdot \left(r + 10\right)} \cdot r \cdot 3
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22,389 |
A\cdot \delta\cdot 2 + \delta \cdot \delta = \left(A + \delta\right)^2 - A \cdot A
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8,873 |
{i + k + 1 \choose i} - {i + k \choose (-1) + i} = {i + k \choose i}
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31,620 |
u = \sqrt{\frac{x + 1}{x + (-1)}} \Rightarrow x = \frac{1}{u^2 + (-1)} \cdot \left(u^2 + 1\right) = 1 + \frac{1}{u^2 + (-1)} \cdot 2
|
26,368 |
k \cdot k + (-1) = ((-1) + k) \cdot (1 + k)
|
3,244 |
-3/2*l + l^2/2 = -l + {l \choose 2}
|
-20,215 |
\frac{35*y + 30}{-28*y + 24*(-1)} = -\frac{1}{4}*5*\dfrac{-7*y + 6*(-1)}{-y*7 + 6*(-1)}
|
-26,008 |
\frac{1}{1 - 4i}(9 - i*2) = \frac{1}{-4i + 1}(9 - 2i) \frac{1 + 4i}{4i + 1}
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-20,012 |
\frac{l*15 + 25}{40 + 24*l} = \dfrac{l*3 + 5}{l*3 + 5}*5/8
|
41,813 |
\frac{-\tan^2(\frac{y}{2}) + 1}{\tan^2(\frac{y}{2}) + 1} = \cos(y)
|
5,439 |
144 + b^2 - 24\cdot b = \left(b + 12\cdot (-1)\right)^2
|
-29,702 |
d/dx x^\theta = \theta\cdot x^{\theta + (-1)}
|
-22,266 |
g * g - 7*g + 8*(-1) = (g + 8*(-1))*(1 + g)
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32,465 |
\sin\left(2*x\right) = \sin(x)*\cos(x)*2
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30,198 |
y*a = a*y
|
42,091 |
(x-y)+2y = x - y + y + y = x+y
|
-21,021 |
\frac{1}{10*n}*(-n + 5*(-1))*\frac55 = (-5*n + 25*\left(-1\right))/(50*n)
|
6,615 |
\sin{z} = \cos{z} \implies (e^{i\cdot z} - e^{-z\cdot i})/\left(i\cdot 2\right) = (e^{i\cdot z} + e^{-z\cdot i})/2
|
192 |
y_0^2 = (1 - y_0)^2 + (2 - y_0)^2\Longrightarrow y_0^2 - y_0 \cdot 6 + 5 = 0
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38,387 |
-0.2*0.9*0.5 + 1 = 0.91
|
2,070 |
8881 = (95 + 12)\cdot \left(12\cdot (-1) + 95\right)
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-11,867 |
0.007585 = 7.585 \cdot 0.001
|
10,632 |
1 + 3 + 3^2 + \ldots + 3^{(-1) + x} = ((-1) + 3^x)/2
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13,123 |
y^{f + c} = y^c y^f
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21,315 |
T + 10*\left(-1\right) + 3*(T + 30*\left(-1\right)) = 0\Longrightarrow T*3 + 90*(-1) + T + 10*\left(-1\right) = 0
|
37,402 |
s^2 + (-1) = 1 + s^2 + 2(-1) = 2s
|
26,005 |
v*r*u + u*s*v = \left(r + s\right)*u*v
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12,631 |
\frac{1}{7} \cdot 5 = \frac{5}{7}
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-20,636 |
10/10 \cdot \frac{1}{3 + r} \cdot \left(8 \cdot (-1) - r \cdot 6\right) = \dfrac{1}{r \cdot 10 + 30} \cdot (-r \cdot 60 + 80 \cdot (-1))
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35,992 |
19 = 3^0 + 3 \cdot 3 \cdot 3 - 3 \cdot 3
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-20,040 |
\frac{1}{-x\cdot 6 + 2\cdot \left(-1\right)}\cdot (4 - x\cdot 3)\cdot \tfrac33 = \frac{12 - 9\cdot x}{6\cdot (-1) - 18\cdot x}
|
32,864 |
\cosh(R) = \frac{\mathrm{d}}{\mathrm{d}R} \sinh(R)
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7,031 |
\left(x^{45} = \dfrac{x^{46}}{x} = \frac{1}{x}\Longrightarrow 1/x = 8\right)\Longrightarrow x = \dfrac{1}{8} = 6
|
17,601 |
z^{\frac{1}{q}\cdot \mu} = (z^\mu)^{1/q} = (z^\mu)^{\frac{1}{q}}
|
-23,129 |
-1/2\cdot \dfrac14\cdot 3 = -\dfrac38
|
16,670 |
\left(x - r\right) \left(-r + x\right) = \left(-r + x\right)^2
|
23,095 |
5 = \sqrt{4^2 + \left(-3\right)^2}
|
12,589 |
\frac{2}{6} = \frac16 + 1/6
|
10,686 |
d/dy \csc^2\left(y\times 4\right) = d/dy \csc^2(y\times 4)
|
3,942 |
|y_1 + y + y_2| = |y_1 + y + y_2|
|
17,103 |
\left(C'\cdot j/j\right) \cdot \left(C'\cdot j/j\right) \cdot \left(C'\cdot j/j\right) = \frac{C'^3\cdot j}{j}
|
-4,602 |
-\tfrac{1}{3 \cdot (-1) + x} + \frac{1}{x + 5} \cdot 3 = \frac{1}{15 \cdot (-1) + x^2 + 2 \cdot x} \cdot (14 \cdot \left(-1\right) + 2 \cdot x)
|
-20,674 |
\frac{1}{z*10 + 60*\left(-1\right)}*(54*(-1) + 9*z) = \frac{6*(-1) + z}{z + 6*\left(-1\right)}*\frac{9}{10}
|
-4,180 |
8x^2/11 = x^2*8/11
|
-3,586 |
2*2*2*2*2*2 = 64
|
15,046 |
\frac{z^2}{z-2} = z^2 \frac{1}{z-2}
|
24,821 |
C*B*A = A*B*C
|
-448 |
(e^{\dfrac{\pi*i}{4}*1})^{12} = e^{12*i*\pi/4}
|
24,127 |
4500 = (1 + 9999 + 1000\cdot (-1))/2
|
28,146 |
\left(x\cdot y\right)^2 = x \cdot x\cdot y \cdot y
|
16,241 |
\binom{r}{i} = \dfrac1i\binom{r + (-1)}{i + \left(-1\right)} r
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3,586 |
0.0625\cdot 0.8888 = 0.0625\cdot \left(0.0001 + \dotsm + 0.1111\right)
|
38,634 |
\dfrac{W\pi}{\pi} = W
|
15,301 |
\arccos\left(x\right) = X \Rightarrow x = \cos\left(X\right)
|
1,890 |
\frac{1}{2\cdot \sqrt{\pi}} = \frac{1}{(4\cdot \pi)^{1/2}}
|
39,661 |
y^2 = l \Rightarrow y = \sqrt{l}
|
-22,930 |
5\cdot 8/(5\cdot 9) = 40/45
|
-30,573 |
\frac{1}{t + 5*(-1)}*(t^2 - 3*t + 10*(-1)) = \frac{1}{t + 5*(-1)}*(t + 2)*(t + 5*(-1)) = t + 2
|
28,674 |
\left(h^3 = b\cdot b\cdot h \Rightarrow (b\cdot h\cdot b)^k = b\cdot h^k\cdot b = h^{3\cdot k}\right) \Rightarrow h^k\cdot b = b\cdot h^{3\cdot k}
|
-18,984 |
5/8 = A_p/\left(100\cdot \pi\right)\cdot 100\cdot \pi = A_p
|
1,269 |
det\left(A \cdot F\right) = det\left(F \cdot A\right)
|
5,565 |
\binom{7}{2}*\binom{5}{2}*3! = 7!/\left(2!*2!\right)
|
21,066 |
\left(-1\right) + l + m = l + (-1) + m
|
9,430 |
6*(-1) + 9 = 3 \implies 15 = 6*\left(-5\right) + 9*5
|
22,793 |
x \cdot q + (-1) - x + q + 2 \cdot \left(-1\right) = x \cdot q - x - q + 1 = (x + (-1)) \cdot (q + (-1))
|
8,583 |
\frac{(-1)^n}{(-1)^{n*2}} = \frac{1}{(-1)^n}
|
27,288 |
(x_i + 1) \cdot (x_k + \left(-1\right)) = x_i \cdot x_k + x_k - x_i + (-1) > x_i \cdot x_k
|
3,626 |
a^2 = h^3 = g^3 = a \cdot h \cdot g
|
-18,252 |
\tfrac{1}{(4\cdot (-1) + a)\cdot a}\cdot (a + 4\cdot (-1))\cdot \left(3 + a\right) = \dfrac{1}{-a\cdot 4 + a^2}\cdot (a^2 - a + 12\cdot (-1))
|
13,821 |
-\frac{1}{\xi^2} = \frac{\text{d}}{\text{d}\xi} \frac{1}{\xi}
|
26,810 |
0 = \left(0 + 1\right)\cdot \frac12\cdot 0
|
32,027 |
x \cdot y \cdot r = r \cdot x \cdot y
|
3,276 |
T^{x + k} = T^x\cdot T^k
|
522 |
5 - 0 \cdot 3 + 9/3 = 5 + 0(-1) + 9/3 = 5 + 0\left(-1\right) + 3 = 5 + 3 = 8
|
33,747 |
2^{\frac13 \cdot 2} = 2^{2/3}
|
13,668 |
\cos(\lambda) = \frac{1}{\cos(\lambda)} \times \left(1 - \sin^2(\lambda)\right)
|
5,020 |
|x| = \sqrt{x \cdot x} < \sqrt{x^2 + 1}
|
-20,076 |
\dfrac{9 - n}{n \cdot 6 + 54 \cdot (-1)} = \frac{9 \cdot (-1) + n}{n + 9 \cdot (-1)} \cdot (-1/6)
|
30,597 |
\frac{20}{20}\times 2 = 2
|
-13,086 |
2 \cdot (-2) = 2 \cdot (-2)/(1) = -4/1
|
448 |
n^2 + m^2 = a^2 + b^2 = (n - a)^2 + (m - b)^2
|
17,255 |
\binom{m + 2}{1 + m} = \binom{m}{m} + \binom{1 + m}{m}
|
32,511 |
(1 + n)! - n! = nn!
|
1,611 |
\dfrac{1}{10} = \dfrac{1}{8} \cdot \frac{4}{5}
|
19,524 |
3*3/4/1 = 9/4
|
-4,565 |
(2 + y) \cdot (y + 3) = y^2 + y \cdot 5 + 6
|
12,500 |
a^{∞} \cdot a = a^{∞}
|
29,527 |
i + (-1) + k - i = (-1) + k
|
31,925 |
A - E \cup Y = A \cap E \cup Y^\complement = Y^\complement \cap (A \cap E^\complement) = E^\complement \cap \left(A \cap Y^\complement\right) = A - Y - E
|
31,525 |
b_J = \overline{\overline{b_J}}
|
30,471 |
\frac14 \cdot (\sqrt{5} - 1) = \cos(2 \cdot π/5)
|
17,900 |
(d^T Ub)^T = b^T U^T d = b^T Ud
|
7,531 |
\mu*g + x^2 + (\mu + g)*x = \left(\mu + x\right)*(g + x)
|
13,333 |
0 = (-52)^2 + 52 \cdot \left(-52\right)
|
-22,265 |
(5 (-1) + t) (t + 10 (-1)) = t^2 - t\cdot 15 + 50
|
9,651 |
\lim_{h \to 0} \mathbb{E}\left(y\right) \cdot (\mathbb{E}\left(h\right) + (-1)) \cdot \cdots = \lim_{h \to 0} \mathbb{E}\left(h + y\right) - \mathbb{E}\left(y\right)
|
-29,935 |
\frac{\mathrm{d}}{\mathrm{d}z} \left(-z^3\right) = -\frac{\mathrm{d}}{\mathrm{d}z} z^3 = -3z^2 = -3z^2
|
37,413 |
(z + 3)\cdot (3\cdot (-1) + z) = z \cdot z + 9\cdot (-1)
|
41,369 |
111 = 258 + 147*\left(-1\right)
|
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