id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
4,730 |
-c/d + \frac1b\cdot a = \frac{1}{d\cdot b}\cdot (a\cdot d - b\cdot c)
|
27,357 |
0 = 1 - 4*z^3 \Rightarrow \frac{1}{4} = z^3
|
32,992 |
\dfrac{{l \choose c}^2}{{l \choose c}} = {l \choose c}
|
11,973 |
g - b + l = l - b + g
|
21,574 |
V*H = H*V
|
-1,967 |
\frac{5}{4}\cdot \pi = \pi + \dfrac14\cdot \pi
|
-7,895 |
(15 \cdot i + 12)/(-3) = 12/(-3) + \frac{i}{-3} \cdot 15
|
29,602 |
\sin(\dfrac12\cdot 3\cdot \pi + x) = -\cos\left(x\right)
|
-6,687 |
\frac{4}{100} + \frac{40}{100} = \frac{4}{100} + \dfrac{4}{10}
|
16,265 |
\operatorname{acos}\left(1/2\right) = \dfrac{\pi}{3}
|
4,804 |
x = \frac{p}{4} + \frac{x}{4} + \dfrac12*0 = \frac14*p + x/4
|
11,871 |
u + 1 > t,t + 1 > u\Longrightarrow u = t
|
40,163 |
vxy + \theta x' + \theta \mu = \theta v + vyx + x' \theta + \theta \mu
|
19,440 |
\dfrac{1}{x^4} + 2*x^2 = \frac{1}{x^7}*(x^3 + x^9*2)
|
80 |
\sqrt{\frac{1}{2}}\times (1 + \sqrt{1/2}) = \frac{1}{2} + \sqrt{1/2} \gt 1
|
3,231 |
1 - \frac{1}{16} = \frac{1}{16}*15
|
12,862 |
\sin{ix} = \left(e^{-x} - e^x\right)/\left(2i\right) = i\sinh{x}
|
-20,627 |
(28*y + 63*(-1))/((-1)*14*y) = (y*4 + 9*(-1))/((-1)*2*y)*7/7
|
-20,297 |
\tfrac{1}{t + 4}*(t + 4)/9 = \dfrac{t + 4}{9*t + 36}
|
-29,609 |
d/dx \left(2x^4\right) = 2\frac{d}{dx} x^4 = 2\cdot 4x \cdot x \cdot x = 8x^3
|
11,434 |
\frac{\partial}{\partial x} F_1 + \frac{\partial}{\partial x} F_2 = \frac{\partial}{\partial x} \left(F_1 + F_2\right)
|
-3,275 |
112^{\frac{1}{2}} - 7^{1 / 2} + 28^{\frac{1}{2}} = (4*7)^{1 / 2} + (16*7)^{\dfrac{1}{2}} - 7^{1 / 2}
|
14,845 |
l^2 \cdot 17 = (4 \cdot l)^2 + l \cdot l
|
4,088 |
a\cdot x\cdot g = a\cdot (x + g + 2\cdot x\cdot g) = a + x + g + 2\cdot x\cdot g + 2\cdot a\cdot x + 2\cdot a\cdot g + 4\cdot a\cdot x\cdot g
|
1,407 |
44 = 5! (-1/5! + 1 - 1/1! + 1/2! - \dfrac{1}{3!} + 1/4!)
|
10,863 |
\frac{8}{x^2 + 1} = d/dx \tan^{-1}(x)*8
|
18,506 |
\dfrac{300}{10} \cdot 3 = 90
|
-10,726 |
-(4\cdot r + 5)/r\cdot \dfrac22 = -\frac{1}{2\cdot r}\cdot (r\cdot 8 + 10)
|
10,909 |
47/15 = \frac{1}{8 + 7} \cdot (22 + 25)
|
-3,334 |
10^{1/2} \cdot \left(4 + 5\right) = 10^{1/2} \cdot 9
|
16,144 |
\frac12 (-\frac12 \pi + \tfrac{1}{2} \pi) = 0
|
12,000 |
1 = xC \Rightarrow \frac1x = C
|
11,703 |
y + y \cdot 2 = y \cdot 3
|
9,243 |
2,(k \cdot \sin\left(A\right))^2 \cdot (k \cdot \sin(A)) = \cos^2\left(A\right) \cdot (\cos^2(A))^2 = \left(k^2 \cdot l\right)^2 \Rightarrow \sin^3(A) = l^2 \cdot k
|
22,376 |
\mathbb{E}(T \cdot \cos(A + x \cdot p)) = \mathbb{E}(T) \cdot \mathbb{E}(\cos(x \cdot p + A))
|
8,495 |
\sin(t) = \sin(π - t)
|
39,448 |
3 = \sqrt{\frac2f \cdot x} - \sqrt{\dfrac{x}{f} \cdot 3 \cdot \frac{1}{2}} = \sqrt{\dfrac{x}{f}} \cdot (\sqrt{2} - \sqrt{3/2})
|
30,942 |
c_1*c_2*H = c_1*H*c_2
|
13,498 |
\frac1BB = 1 \Rightarrow \tfrac1B = 1/B
|
37,668 |
\frac{1}{l_1 \cdot l_2} = \frac{1}{l_1 \cdot l_2}
|
4,194 |
\frac{1}{\pi \cdot 8} \cdot \frac{4}{27} = \frac{1}{\pi \cdot 54}
|
-20,659 |
\frac{\left(-24\right) \cdot m}{30 \cdot m} = \frac{m \cdot 6}{6 \cdot m} \cdot (-4/5)
|
33,184 |
40/7 = 42/7 - \frac{1}{7}\times 2
|
-7,117 |
3/10\cdot \tfrac29 = \dfrac{1}{15}
|
21,646 |
\sin{x}\cdot \cos{\beta} + \sin{\beta}\cdot \cos{x} = \sin(\beta + x)
|
36,800 |
f_2\cdot f_1 + f_1\cdot b + b\cdot f_2 = \left(-(f_1^2 + b^2 + f_2 \cdot f_2) + (f_2 + f_1 + b) \cdot (f_2 + f_1 + b)\right)/2
|
8,378 |
S^2 \cdot b = b \cdot S^2
|
5,106 |
4 \cdot z^2 + 9 \cdot y^2 = 180 \Rightarrow y^2/20 + z^2/45 = 1
|
16,949 |
\frac{1}{2} \cdot (3^n + (-1)) = 1 + 3 + 3^2 + \ldots + 3^{n + (-1)}
|
17,408 |
\cot\left(5\pi/14\right) = \cot\left(\dfrac{\pi}{2} - \frac{1}{7}\pi\right)
|
13,441 |
1/n = \frac{1}{n!}\times (n + (-1))!
|
28,847 |
-\frac{1}{4} \cdot \pi = \arctan{-1}
|
21,873 |
\left(1 + 1 + 2\cdot k - 6\cdot k + 10\cdot (-1) = 0 \Rightarrow -k\cdot 4 + 8\cdot (-1) = 0\right) \Rightarrow -2 = k
|
3,301 |
\left(y + 1 = y \Rightarrow y^2 + y*2 + 1 = y^2\right) \Rightarrow 0 = y*2 + 1
|
9,032 |
-\cot(x) = \cot\left(-x + \pi\right)
|
5,335 |
(x + 3)\cdot (5\cdot \left(-1\right) + x) = (x - -3)\cdot (5\cdot \left(-1\right) + x)
|
-22,765 |
\frac{18}{30} = \frac{3}{5*6}*6
|
35,422 |
\dfrac{2\times \pi}{3} - \pi = \frac13\times \left(\left(-1\right)\times \pi\right)
|
36,791 |
\frac{W}{m^2 k} = \frac{\dfrac{W}{km}}{m}
|
-19,088 |
44/45 = A_s/(81 \pi) \cdot 81 \pi = A_s
|
22,388 |
\tfrac{1}{\cos(\theta)}*\sin(\theta) = \tan(\theta)
|
8,974 |
4 + 48 (-1) + 2 + y''' = 0 \implies 42 = y'''
|
-20,963 |
(-6 \cdot x + 2 \cdot (-1))/(-10) \cdot \frac99 = (-54 \cdot x + 18 \cdot (-1))/(-90)
|
-10,303 |
-\frac{24}{r \cdot 8 + 20} = -\dfrac{1}{r \cdot 2 + 5} \cdot 6 \cdot 4/4
|
19,406 |
\frac14*x + 3/4*z = (\dfrac12*(x + z) + z)/2
|
29,557 |
e + e = e\cdot 2
|
25,921 |
m*n + (m + n)*3 = 0 \Rightarrow 9 = (3 + m)*\left(n + 3\right),m,0 \geq n
|
-2,608 |
\sqrt{9*2} + \sqrt{16*2} = \sqrt{18} + \sqrt{32}
|
9,148 |
0 = H_2\cdot H_1 - H_2\cdot H_1 = \frac{B}{j}\cdot H_2 - \dfrac{B\cdot H_1}{x} = (H_2\cdot B\cdot x - j\cdot B\cdot H_1)/(x\cdot j)
|
7,775 |
-(n^2 + (-1))^2 + (1 + n^2)^2 = 4\cdot n \cdot n
|
8,872 |
\frac{3^{-n}}{3} = 3^{-(n + 1)}
|
9,475 |
\frac{1}{a/x - \dfrac{b}{x}} = \frac{x}{a - b}
|
27,990 |
0 \leq 9^{1/2} \implies 3 = 9^{\tfrac12}
|
10,534 |
\frac{1}{2} + 1 = \dfrac{1}{2}\cdot 3
|
-6,641 |
\dfrac{1}{(z + 1)*(z + 7)}*4 = \frac{4}{z * z + 8*z + 7}
|
7,655 |
2^{2^k + 2^n} = 2^{2^k} \cdot 2^{2^n}
|
9,079 |
5\cdot (13\cdot (-1) + m) + 71 = 5\cdot m + 6
|
-12,321 |
27^{1/2} = 3^{1/2}*3
|
8,775 |
m p x = x p m
|
36,721 |
(b^2 + f' \cdot f')^{\frac{1}{2}} = (f' \cdot f' + b^2)^{1 / 2}
|
30,916 |
l/2 + 1 + \frac{l}{2} + 1 = 2 + l
|
-16,750 |
3 = 3*3 p + 3 (-7) = 9 p - 21 = 9 p + 21 \left(-1\right)
|
-11,082 |
(x + 5*(-1))^2 + a = (x + 5*(-1))*\left(x + 5*(-1)\right) + a = x^2 - 10*x + 25 + a
|
7,144 |
\binom{(-1) + x}{l + (-1)}*\frac{1}{l}*x = \binom{x}{l}
|
32,987 |
\dfrac{45}{216} = \frac{1}{24}\cdot 5
|
22,609 |
\cos\left(y + \pi \cdot 2\right) = \cos(y)
|
-22,201 |
72 (-1) + p p - p = (p + 9 (-1)) \left(p + 8\right)
|
400 |
1 + 3 \cdot x = \frac{1}{\left(1 - x\right)^8} \cdot \left(1 + 3 \cdot x\right)
|
25,121 |
2 - 9 x^7 + 7 x^9 = (1 - x) (1 - x) (2 + 4 x + 6 x^2 + 8 x^3 + 10 x^4 + 12 x^5 + 14 x^6 + 7 x^7) \approx 63 \left(1 - x\right)^2
|
26,441 |
(r + \sqrt{2})\cdot \left(-\sqrt{2} + r\right) = r^2 + 2\cdot \left(-1\right)
|
2,731 |
\left(b a\right)^1 = b a
|
10,299 |
(1+x)^n(1+x)^n = (1+x)^{2n}
|
29,884 |
a + c \cdot i = a + c \cdot i
|
19,664 |
d_{n + (-1)}*d_n^{m + (-1)}*\binom{m}{1}*a_m = m*a_m*d_n^{(-1) + m}*d_{(-1) + n}
|
19,927 |
a^2 + r^2 + 2\cdot a\cdot r = (a + r)^2
|
4,678 |
y \cdot y + 2\cdot J^2 + J\cdot y\cdot 2 = J^2 + (J + y)^2
|
20,145 |
5^3 + 50 + 5(-1) + 2(-1) = 168 = 4 \cdot 42
|
-6,423 |
\frac{2}{2 + 2 \cdot t} = \frac{2}{2 \cdot (1 + t)}
|
-16,393 |
5\cdot 9^{1/2}\cdot 13^{1/2} = 5\cdot 3\cdot 13^{1/2} = 15\cdot 13^{1/2}
|
-19,044 |
\tfrac{5}{8} = \frac{1}{4\pi}H_x*4\pi = H_x
|
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