id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
15,598 |
2*\sin(\frac12*x)*\cos(\dfrac{1}{2}*x) = \sin(x)
|
24,826 |
\frac{1}{1+\frac{a}{x}} = \frac{x}{a+x}=\frac{-a + a +x}{a+x} = 1 - \frac{a}{a+x}
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26,072 |
x\cdot x! = \left(x + 1 + (-1)\right)\cdot x! = (x + 1)! - x!
|
12,267 |
1 \geq \frac1l \Rightarrow 2 \geq 1 + 1/l
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26,820 |
\left((-6) + 9 \cdot B = 3 \implies 9 \cdot B = 3 + 6\right) \implies B = 1
|
24,547 |
n \cdot 5 + 1 + n \cdot 7 + 1 = 2 + n \cdot 12
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-22,291 |
\left(x + 2\times \left(-1\right)\right)\times \left(x + 9\times (-1)\right) = x^2 - x\times 11 + 18
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8,215 |
-2\cdot x \cdot x + 8\cdot z = 0 rightarrow z\cdot 4 = x^2
|
22,013 |
2 = 1\cdot 2 = \left(4 + 2\right)\cdot (4 + 2\cdot (-1)) = 4^2 - 2^2
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-16,381 |
(25\times 13)^{1 / 2}\times 2 = 2\times 325^{1 / 2}
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13,600 |
\frac{1}{3} + \frac{2}{9} = 3/9 + \dfrac{2}{9} = 5/9
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368 |
\tfrac{1}{2 \cdot 2} + \frac{1}{3 \cdot 2} = 5/12
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6,579 |
100*17 * 17 + 17*20 = 73*100*2^2 + 2*20
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21,466 |
1/(bg) = \dfrac{1}{bg}
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5,812 |
1^i = e^{2x\pi i i} = e^{-2x\pi}
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-4,458 |
\frac{1}{z^2 + 3 \cdot z + 10 \cdot (-1)} \cdot (z \cdot 3 + 20 \cdot (-1)) = -\frac{1}{z + 2 \cdot (-1)} \cdot 2 + \dfrac{5}{z + 5}
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36,931 |
\frac{\partial}{\partial x} (c_2 \cdot c \cdot c_1) = c \cdot c_2 \cdot \frac{\partial}{\partial x} c_1 + c \cdot c_1 \cdot \frac{\partial}{\partial x} c_2 + c_2 \cdot c_1 \cdot \frac{\text{d}c}{\text{d}x}
|
4,275 |
x^4 + \left(-1\right) = \left(x^2 + \left(-1\right)\right) \cdot (x^2 + 1) = \left(x + (-1)\right) \cdot \left(x + 1\right) \cdot (x^2 + 1)
|
17,919 |
-1/8 + 1/2 = \dfrac18\cdot 3
|
-4,765 |
-\frac{1}{4 + y} \cdot 5 - \dfrac{1}{y + 2} \cdot 3 = \frac{-8 \cdot y + 22 \cdot (-1)}{y \cdot y + y \cdot 6 + 8}
|
5,260 |
\binom{5}{4}\cdot 1^5 + 5^5 - 4^5\cdot \binom{5}{1} + 3^5\cdot \binom{5}{2} - \binom{5}{3}\cdot 2^5 = 5!
|
23,004 |
eae = aee
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-10,607 |
-\frac{k\cdot 20 + 8}{k^2\cdot 4} = \frac44\cdot (-\dfrac{1}{k^2}\cdot (2 + k\cdot 5))
|
-11,763 |
(\frac17*10)^2 = \frac{100}{49}
|
27,980 |
2^{m + 1} + 2^{m + 1} = 2 \cdot 2^{m + 1}
|
25,832 |
\frac{1}{6}\cdot 5/7 = \frac{5}{42}
|
27,822 |
x \cdot D = x \cdot D
|
3,150 |
\frac{1}{11 + y} \cdot (y \cdot y + y \cdot 9 + a) = y + 2 \cdot \left(-1\right) + \frac{22 + a}{11 + y}
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21,094 |
\frac{a*1/b}{c} = a*1/b/c = \frac{a}{b*c}
|
5,060 |
-1 = \frac{1}{-1} \cdot \left(2 \cdot |-1| - (-1)^2\right)^{1/2}
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-20,575 |
\frac{18 + 9*g}{16*(-1) - g*8} = \frac{-g + 2*(-1)}{-g + 2*(-1)}*(-9/8)
|
14,065 |
z^3 + 3\cdot z^2 + 6 = (z + 1)^3 - 3\cdot z + (-1) + 6 = (z + 1) \cdot \left(z + 1\right)^2 - 3\cdot (z + 1) + 8
|
5,626 |
67 = 1 + 11 \times 2 \times 3
|
1,041 |
(x^k)^{12} = 1 \Rightarrow x^k
|
8,404 |
((-1) + n) \cdot n = n^2 - n
|
14,207 |
\frac1I = 1/(\dfrac{1}{\dfrac1I})
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38,630 |
P*((-1) + 3) + a = 2*P + a
|
5,421 |
\operatorname{E}[R_D]*\operatorname{E}[R_H] = \operatorname{E}[R_D*R_H]
|
-25,818 |
5/40 = \dfrac{5}{4 \cdot 10}
|
26,587 |
x! \dfrac{x}{((-1) + x)!} = x^2
|
-30,319 |
6*(-1) + 8 = 2
|
1,052 |
\left(a + b\right)*(a^2 - a*b + b^2) = a^3 - a^2*b + a*b * b + a * a*b - a*b^2 + b^3 = a^3 + b^3
|
35,406 |
\sqrt{(-5) \cdot (-5)} = \sqrt{25} = 5
|
31,007 |
f + w + f + w = 2*(f + w) = 2*f + 2*w = f + f + w + w = f + f + w + w
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-11,557 |
-5 + 8\times (-1) + 18\times i = -13 + i\times 18
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27,874 |
\frac1x \times \left(\sqrt{1 + x + x^2} + \left(-1\right)\right) = -\frac1x + \sqrt{1 + x + x \times x}/x
|
17,092 |
m^2 + m + 1 = 1 + (1 + m) \cdot (1 + m) - 1 + m
|
-1,387 |
((-1)*1/9)/(\frac{1}{7}*9) = -1/9*\frac79
|
14,073 |
\frac{\sinh(y)}{\cosh(y)} = \tanh\left(y\right)
|
-20,815 |
\frac{c + 5 \cdot (-1)}{5 \cdot (-1) + c} \cdot (-\frac17) = \frac{5 - c}{7 \cdot c + 35 \cdot (-1)}
|
-22,384 |
11*\left(-1\right) + 6 = -5
|
1,662 |
-2 \cdot \frac{f'}{a^3} = \frac{f'}{a} \cdot \frac{f'}{a} \cdot 2
|
15,739 |
(3^{19} - 2^{20} + 1) \cdot 3 = 3^{20} - ((-1) + 2^{20}) \cdot 3
|
4,629 |
1 = \frac{1}{2^{\frac{1}{2}}}\cdot 2^{1 / 2}
|
-15,617 |
\frac{k^{15}}{k\cdot \frac{1}{a^2}} = \dfrac{1}{\frac{1}{a^2}\cdot k\cdot \frac{1}{k^{15}}}
|
14,599 |
\left(n^4*2 - 2n * n + 1\right)^2 + (n*2 + n^5 - 2n^3) * (n*2 + n^5 - 2n^3) = 1 + n^{10}
|
10,097 |
\tan{2 \times x} + \tan{x} = 0\Longrightarrow \tan{x} = 0
|
2,967 |
(1 - d) \cdot (1 - e) = 1 - d - e + d \cdot e \geq 1 - d - e
|
-7,712 |
\frac{1}{25}\cdot (104 - 28\cdot i + 78\cdot i + 21) = \frac{1}{25}\cdot (125 + 50\cdot i) = 5 + 2\cdot i
|
-2,732 |
5*\sqrt{7} + 2*\sqrt{7} = \sqrt{4}*\sqrt{7} + \sqrt{25}*\sqrt{7}
|
-20,015 |
\frac{r + 9*(-1)}{-r*2 + 3}*\frac{6}{6} = \frac{54*\left(-1\right) + r*6}{18 - r*12}
|
12,349 |
1 - 3 \cdot s + 3 \cdot s^2 - s^3 = (1 - s)^2 \cdot \left(1 - s\right)
|
33,058 |
\frac13\cdot 6\cdot 2 = 6/3\cdot 2
|
38,291 |
303 = 30\cdot 10 + 3
|
27,167 |
1.0 = 1.0 = ... = 1 \cdot ...
|
6,467 |
\left((-1) + k\right)\cdot 2 + 1 = (-1) + 2\cdot k
|
-30,542 |
\frac{dy}{dx} = \dfrac{1}{y \cdot x^3} = \frac{1}{x^3 \cdot y}
|
5,927 |
y^6 + \left(-1\right) = (1 + y^4 + y^2) \cdot (y^2 + (-1))
|
-2,847 |
\sqrt{4} \cdot \sqrt{3} + \sqrt{3} = \sqrt{3} + \sqrt{3} \cdot 2
|
28,432 |
I + x \cdot E = \left(x + 1\right) \cdot (-\frac{x}{1 + x} \cdot (-E + I) + I)
|
21,666 |
\left(x = (d + x)^{\dfrac{1}{2}} \Rightarrow x * x - x - d = 0\right) \Rightarrow \frac{1}{2}*\left((1 + 4*d)^{\frac{1}{2}} + 1\right) = x
|
6,844 |
q^2 - q = q*(1 + q) - q - q + 1 + 1
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-20,926 |
\frac{-k\cdot 2 + 9\cdot (-1)}{-2\cdot k + 9\cdot (-1)}\cdot \dfrac{1}{10}\cdot 3 = \tfrac{-6\cdot k + 27\cdot \left(-1\right)}{90\cdot (-1) - 20\cdot k}
|
23,143 |
(x^2 + 6\cdot x + 6) \cdot (x^2 + 6\cdot x + 6) - x^2 = (1 + x)\cdot (x + 6)\cdot (x + 3)\cdot (x + 2)
|
4,172 |
\frac{10\cdot \pi^3}{81\cdot \sqrt{3}} = 10\cdot \pi \cdot \pi^2\cdot \sqrt{3}/243
|
16,115 |
5 \cdot a + \sqrt{5} \cdot b = \sqrt{5} \cdot (b + a \cdot \sqrt{5})
|
-9,267 |
-27\cdot a + a^2\cdot 30 = a\cdot 2\cdot 3\cdot 5\cdot a - 3\cdot 3\cdot 3\cdot a
|
23,256 |
10 + 10^3\cdot 3 - 3\cdot 10^2 = 2710
|
-22,204 |
2 + k^2 - k\cdot 3 = \left(k + (-1)\right)\cdot (k + 2\cdot (-1))
|
1,845 |
1 = -B \cdot 4\Longrightarrow -1/4 = B
|
-22,055 |
\frac{1}{12} \times 28 = \frac13 \times 7
|
26,898 |
(x^2 + 13/25)\cdot 25 = 13 + 25\cdot x^2
|
20,995 |
-\sin{-\psi}\cdot (-1) = \sin{-\psi} = -\sin{\psi}
|
31,915 |
\left((-1) + x\right)^2 = x^2 - 2*x + 1 \Rightarrow (-1) + (x + (-1))^2 = -x*2 + x^2
|
13,257 |
(-1)*4 + 9 = \frac{(-1)*8}{2} + 9
|
-29,348 |
x\cdot \left(-4\right) (x + 6(-1)) = x^2 - 6x - 4x + 24 = x \cdot x - 10 x + 24
|
5,146 |
-\dfrac{t^3}{1 + t} + 1 - t + t^2 = \frac{1}{1 + t}
|
17,665 |
i + k < l \Rightarrow i < l - k
|
9,802 |
\frac{-q^{2k} + 1}{1 - q^k} = q^k + 1
|
6,300 |
\sqrt{g_2} \cdot \sqrt{g_2} \cdot \sqrt{g_1} \cdot \sqrt{g_1} = g_2 \cdot g_1
|
31,982 |
1010 \cdot x - x \cdot 404 = x \cdot 606
|
18,556 |
1 - \mathbb{P}\left(A\right) - \mathbb{P}\left(H\right) + \mathbb{P}(A) \cdot \mathbb{P}(H) = \left(1 - \mathbb{P}(A)\right) \cdot \left(-\mathbb{P}\left(H\right) + 1\right)
|
-6,465 |
\frac{1}{4 (q + 8)} = \frac{1}{32 + 4 q}
|
-20,023 |
(7 - a*56)/14 = (1 - 8a)/2*\frac{7}{7}
|
11,101 |
\sec{x}*p = r*\csc{x} \implies \frac{r}{p} = \tan{x}
|
33,825 |
e^{\dfrac12 \cdot ((-1) \cdot \theta)} = (e^{\frac{1}{4} \cdot ((-1) \cdot \theta)})^2
|
14,979 |
6 + 2*((-5)^{1 / 2} + 1) = 8 + 2*\left(-5\right)^{\frac{1}{2}}
|
9,091 |
\frac{g^l}{z}*z = (z*\tfrac{1}{z}*g)^l
|
39,123 |
(a + b)^2 = a \cdot a + 2ab + b^2 \geq a^2 + b^2
|
12,054 |
2 \sin{i} \sin{D} = -\cos(D + i) + \cos(-D + i)
|
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