id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-26,434 |
64/7 = -\frac{1}{7}*16*(-4)
|
18,115 |
x - j + m = x - j - m
|
7,510 |
x^2 + y^2 + z^2 = 2xyz \implies x = y = z = 0
|
2,353 |
\sin(\alpha)\cdot \sin(\beta) + \cos(\alpha)\cdot \cos(\beta) = \cos(-\beta + \alpha)
|
33,679 |
\dfrac{q^{5 + (-1)}\cdot s^{(-1) + 7}}{s^{6 + (-1)}\cdot q^{\left(-1\right) + 4}}\cdot r^{3 + (-1)} = q^{2 + (-1)}\cdot s^{(-1) + 2}\cdot r^{3 + (-1)}
|
16,004 |
{n \choose m} = \frac{n!}{m! (n - m)!}
|
11,205 |
1 + t^4 = (t^2 + \left(-1\right)) * (t^2 + \left(-1\right)) + 2t * t
|
24,626 |
790 = (250 * 3) + ((3 - 1) * 20)
|
1,440 |
\dfrac{1}{\frac{7}{z^2} + 1/z}\cdot ((-1) + \frac{1}{z^3}) = \dfrac{1 - z^3}{z\cdot 7 + z \cdot z}
|
-7,436 |
1/3 = \frac{6}{10}*5/9
|
-3,286 |
(5 + 3*(-1))*2^{1/2} = 2^{1/2}*2
|
-3,143 |
(1 + 4)\cdot \sqrt{13} = \sqrt{13}\cdot 5
|
29,890 |
\frac{(-1) + z}{\left((-1) + z\right)^2} = \frac{1}{z + (-1)}
|
7,032 |
\sqrt{13}*n - \dfrac{n*5}{\sqrt{13}} = \frac{8*n}{\sqrt{13}}
|
6,598 |
4 \cdot x^5 = Q^2 - y \cdot y \Rightarrow 4 \cdot x^5 = (Q - y) \cdot (y + Q)
|
12,659 |
|z_2 - z_1| = z_1 - z_2 = \frac{z_1^2 - z_2^2}{z_2 + z_1} < \left(z_1^2 - z_2 \times z_2\right)/(2\times z_2)
|
15,351 |
\cos(y + z) = \cos(z) \times \cos(y) - \sin(y) \times \sin(z)
|
-4,634 |
\dfrac{1}{25 (-1) + y \cdot y}(10 + 8y) = \dfrac{3}{y + 5} + \tfrac{5}{y + 5(-1)}
|
31,139 |
π\cdot 2\cdot \frac{1}{3}/(2\cdot π) = 1/3
|
36,887 |
11 + 5*(-1) + 3*(-1) = 3
|
7,085 |
x \cdot x^2 + y^3 + z^3 - y\cdot z\cdot x\cdot 3 = (x^2 + y \cdot y + z^2 - y\cdot x - y\cdot z - x\cdot z)\cdot (z + x + y)
|
6,792 |
\pi/6 = \pi\times 2/12
|
-21,598 |
\cos{-\pi*\frac53} = 0.5
|
33,680 |
-(y + (-1))*(3*(-1) + y) = -y^2 + y*4 + 3*(-1)
|
25,287 |
\tfrac{3}{7} + \frac{1}{42}5 = \dfrac{1}{42}18 + \frac{1}{42}5 = 23/42
|
20,566 |
165 = {8 + 4 + \left(-1\right) \choose (-1) + 4}
|
33,195 |
\frac{1}{4\times \left(-1\right) + 8}\times (28 + 8\times (-1)) = 5
|
28,695 |
255\cdot (-1) + 32\cdot x - 2\cdot 0 = 0 \Rightarrow \frac{255}{32} = x
|
-4,483 |
\frac{1}{y^2 - 5y + 6}(6y + 17 (-1)) = \frac{1}{y + 3(-1)} + \tfrac{5}{y + 2(-1)}
|
26,876 |
210 + 360 + 90 + 10 + 45 = 715
|
5,001 |
2/9 = 4*\frac19/2
|
11,637 |
\frac{L}{2} = L \Rightarrow 0 = L
|
16,984 |
z^a \cdot z^b = z^{a + b}
|
13,327 |
s + (-1) + k + 2 \cdot (-1) = 3 \cdot \left(-1\right) + s + k
|
2,809 |
1 - \frac{1}{n + 1} = \frac{n + 1}{1 + n} - \frac{1}{1 + n}
|
15,875 |
-i = 0 - i = \cos{\dfrac32 \cdot π} + \sin{\frac{π}{2} \cdot 3} \cdot i
|
15,999 |
(1 + z^2 - 3^{\frac{1}{2}} \times z) \times (z^2 + z \times 3^{\frac{1}{2}} + 1) = z^4 - z^2 + 1
|
11,852 |
\cot{\theta} = -\tan(-\frac12 \cdot \pi + \theta)
|
18,235 |
x^3 = -2x + (-1) = x + 2
|
28,264 |
2\cdot l + 2\cdot (-1) = 2\cdot (\left(-1\right) + l)
|
-1,676 |
\dfrac{\pi}{4} + \pi \cdot 3/2 = \frac74 \pi
|
111 |
3/7 = \dfrac{1}{{7 \choose 3}}*{6 \choose 2}
|
20,575 |
\sin(\mathbb{E}[X]) = \mathbb{E}[\sin\left(X\right)]
|
15,188 |
y \cdot y \cdot y \cdot 4 - y \cdot 3 = -\frac{1}{2} \Rightarrow 8 \cdot y^3 - 6 \cdot y + 1 = 0
|
-30,341 |
6 + 3*(-1) = 3
|
-30,854 |
\frac{-5x^2 + 20 x}{-x*4 + x^3 - x^2*3} = -\dfrac{1}{x + 1}5
|
13,158 |
p = \dfrac{1}{n^2}\cdot m^2\Longrightarrow p\cdot n \cdot n = m \cdot m
|
3,777 |
\frac{\mathrm{d}}{\mathrm{d}x} z^3 = 3z^2 \frac{\mathrm{d}z}{\mathrm{d}x}
|
-13,060 |
16 = 26 + 10 \left(-1\right)
|
-4,484 |
(z + 2\cdot (-1))\cdot (3\cdot (-1) + z) = 6 + z^2 - z\cdot 5
|
17,424 |
5 \times \dfrac15 \times \dfrac15 = 1/5
|
-20,396 |
-1/4*\frac{-5*r + 4*(-1)}{-5*r + 4*(-1)} = \frac{4 + r*5}{16*\left(-1\right) - 20*r}
|
17,030 |
z - a < \delta \implies \delta + a > z
|
21,483 |
\left(z^2 = 1 \implies ((-1) + z)^2 = 0\right) \implies 0 = (-1) + z
|
-16,674 |
-1 = -a - 2 = -a - 2 = -a + 2 \left(-1\right)
|
-23,020 |
\frac{3 \cdot 10}{10 \cdot 5} = 30/50
|
-529 |
\left(e^{\pi i \cdot 5/12}\right)^4 = e^{5\pi i/12 \cdot 4}
|
-1,897 |
\frac14*5*\pi = 7/6*\pi + \pi/12
|
16,602 |
\frac{2 \cdot 1/5}{3 \cdot \dfrac15} = \dfrac{1}{5} \cdot 2 \cdot 5/3 = 2/3
|
20,889 |
a_3\cdot x\cdot a_2\cdot x\cdot a_1 = a_1\cdot a_3\cdot x^2\cdot a_2
|
752 |
6 = \frac{1}{\left(2(-1) + 3\right)!}3!
|
7,842 |
\sigma\cdot (v + x) = \sigma v + \sigma x
|
-14,022 |
-\frac{18}{3 + 5 \cdot (-1)} = -\frac{1}{-2} \cdot 18 = -\dfrac{1}{-2} \cdot 18 = 9
|
28,368 |
y^2 - 2y + 1 \geq 0 \implies 2y \leq y^2 + 1
|
-1,605 |
\frac{1}{6}7 \pi - \dfrac{\pi}{2} = \pi \frac132
|
-20,522 |
\frac{9\cdot (-1) + t}{t + 9\cdot (-1)}\cdot 10/7 = \frac{90\cdot (-1) + t\cdot 10}{63\cdot (-1) + 7\cdot t}
|
17,930 |
l*0 = 0 = 0 l
|
4,671 |
\{E_2, E_1\} \Rightarrow E_1 = E_2 \cup E_1 \backslash E_2
|
-27,734 |
-\csc(x)\cdot \cot(x) = d/dx \csc(x)
|
137 |
-\cos{\alpha} = \cos(\alpha + π)
|
26,097 |
-k^2 + (1 + k)^2 = 2\cdot k + 1
|
30,802 |
F = \sqrt{F} \cdot \sqrt{F}
|
16,936 |
(-g + d) \cdot (g + d) = d^2 - g^2
|
23,022 |
6.4 = 2 + 8*0.55
|
23,238 |
\left(a^2 - 2 \cdot a \cdot g + g^2 = (a - g)^2 = 0 \implies 0 = a - g\right) \implies g = a
|
16,263 |
1 = \frac1g + \frac{1}{g + b} + \frac{1}{g + b + c} \geq \frac{3}{g + b + c}
|
-20,515 |
\dfrac{1}{80\cdot (-1) + 8\cdot p}\cdot (-5\cdot p + 50) = -5/8\cdot \frac{p + 10\cdot (-1)}{10\cdot (-1) + p}
|
18,726 |
8 = (\sqrt{a^2 + b^2})^3 \implies (a^2 + b^2) \cdot (a^2 + b^2) \cdot (a^2 + b^2) = 8 \cdot 8 = (2 \cdot 2 \cdot 2)^2 = 2^6
|
26,502 |
x\cdot h = f\cdot g \implies f = h,x = g
|
1,982 |
-z \cdot 84 = 6 \cdot z \cdot (-7) \cdot 2
|
28,639 |
2 + i\sqrt{5} = 2 + \sqrt{-5}
|
29,645 |
-1 = \sin(\dfrac32 \pi)
|
2,669 |
2x + 2\varphi = (x + \varphi)*2
|
25,761 |
\frac98 = \frac{3}{2\cdot 1/3}\cdot \dfrac{1}{4}
|
13,024 |
\tfrac{3}{4}\cdot 3 + \frac{1}{4} = 2.5
|
17,069 |
r^2 + r \cdot r \cdot 2 = r^2 \cdot 3
|
7,595 |
p^l*b = c*x*p\Longrightarrow c*x = b*p^{l + (-1)}
|
21,615 |
(1 - z + z^2)^{3\cdot k}\cdot (1 + z)^{3\cdot k} = ((1 - z + z^2)\cdot (1 + z))^{3\cdot k} = \left(1 + z^3\right)^{3\cdot k}
|
-3,806 |
r^2\cdot 8/5 = \tfrac85\cdot r \cdot r
|
19,631 |
(r_2 + r_1)\cdot m = m\cdot r_2 + m\cdot r_1
|
5,866 |
x^2 + x \cdot 4 + 3 = (x + 3) (x + 1)
|
28,421 |
le x = lx e
|
-7,621 |
\dfrac{3 + 3\cdot i}{3 + 3\cdot i}\cdot \tfrac{3 + 21\cdot i}{-i\cdot 3 + 3} = \frac{21\cdot i + 3}{3 - 3\cdot i}
|
29,531 |
2\cdot 3^{1 + \left(-1\right)} = 2 = 3^1 + \left(-1\right)
|
-26,655 |
\left(7 r^2 + 2\right) (r^2*7 + 2 (-1)) = (7 r^2)^2 - 2^2
|
13,439 |
\sqrt{4 - x^2}/2 = \cos{\theta} \implies \cos{\theta}*2 = \sqrt{-x^2 + 4}
|
-11,729 |
\frac{36}{25} = (\frac{1}{5}*6)^2
|
7,130 |
\frac{10}{23 - -7} = \frac{1}{30} \cdot 10 = \dfrac13
|
38,614 |
\left(-3\right)\cdot \left(-4\right) = 12
|
17,628 |
\frac{1}{-1/2 + \dfrac{1}{A_x} \cdot A_{2 \cdot x + 1}} = \frac{A_x}{-A_x/2 + A_{1 + x \cdot 2}}
|
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