id
int64
-30,985
55.9k
text
stringlengths
5
437k
-29,570
-x = -\frac{1}{x}*x^2
34,407
\binom{\left(-1\right) + r + 10}{10 + (-1)} = \binom{r + 9}{9}
-1,862
\pi/4 = -7/4 \pi + 2\pi
34,347
(x^2 + 2\cdot x\cdot y + y \cdot y - x - y)/2 = {x + y \choose 2}
9,067
m \cdot m - ((-1) + m)^2 = (-1) + m\cdot 2
20,258
\frac{\mathrm{d}y}{\mathrm{d}Z} = \frac{(-2) \cdot Z}{8 \cdot y} = \frac{1}{4 \cdot y} \cdot ((-1) \cdot Z)
34,999
3.75 = \frac14\times 3\times 5
5,106
y \cdot y\cdot 9 + x^2\cdot 4 = 180\Longrightarrow \frac{x^2}{45} + y^2/20 = 1
14,434
\frac{1}{f*F} = 1/(F*f)
15,300
3^l\cdot (y - -\frac{2}{3})^l = (y\cdot 3 + 2)^l
-22,303
8 + q^2 - q*6 = (2*(-1) + q)*(q + 4*(-1))
-30,713
5\cdot (x\cdot 4 + (-1)) = 5\cdot (-1) + x\cdot 20
34,815
\left(\overline{-3} = \overline{a} + \overline{i_1} + \overline{3} \Rightarrow \overline{a} + \overline{i_1} + \overline{3} + \overline{3} = 0\right) \Rightarrow \overline{-a} = \overline{i_1}
11,817
\left(n + 1\right) \cdot n = n^2 + n
-10,527
\frac{2}{2} (-\frac{1}{2y + 10}8) = -\frac{16}{4y + 20}
30,273
3600 - 4*41*49 = 3600 + 8036*(-1) = -4436
-10,679
\frac{15}{x \times 75} = 5/5 \times \frac{3}{x \times 15}
21,665
b^3 + a^3 = \left(b + a\right) (a^2 - ab + b^2)
45,770
\left\lfloor{\frac{1}{6}*100}\right\rfloor = 16
-17,526
18 = 19 \times (-1) + 37
8,358
2 \cdot \sin\left(b\right) \cdot \cos(a) = -\sin(a - b) + \sin(b + a)
8,474
12 \cdot (-1) + (y + 2 \cdot (-1))^2 \cdot 3 = 3 \cdot y^2 - y \cdot 12
14,370
4k + 2n = n^2*2 \Rightarrow n^2*2 = 2*(n + k*2)
33,579
3^x + 3^{x + 2} = 3^x + 3^x 3^2 = 3^x + 9 \cdot 3^x = 10 \cdot 3^x
6,570
2/6 = \tan{h}\Longrightarrow 22 = h
7,799
\emptyset = [1, 2] = 2 \cdot ( 1, 1)
4,745
x^{1/3} = i \cdot r + t \implies (t + i \cdot r)^2 \cdot (t + r \cdot i) = x
4,807
z^2 + z*j*4 + j^2 = (7*z + j*2)^2 - 3*(j + 4*z) * (j + 4*z)
35,501
25 \cdot (-1) + t \cdot 20 = (t - \frac{5}{4}) \cdot 20
9,846
y + z = -y\cdot \left(-1\right) + z
5,542
\cot{-\frac{37}{2} \pi} = 0
16,797
p^2 - p \cdot y \cdot 4 + 4 \cdot y \cdot y = (p - y \cdot 2)^2
-18,774
x = \tfrac{x*7}{7}
22,808
z^{z^{z^{z^{...}}}} = 2 \implies z^2 = 2
12,093
x^2 - 3\cdot x = x^2 - 3\cdot x + (\frac{3}{2})^2 - (3/2)^2 = (x - 3/2)^2 - (\dfrac{3}{2}) \cdot (\dfrac{3}{2})
23,871
|H K|/|H| = \frac{|K|}{|H \cap K|} = K \cap \dfrac{K}{H}
-16,533
9\sqrt{25} \cdot \sqrt{2} = 9 \cdot 5 \cdot \sqrt{2} = 45\sqrt{2}
13,190
B*C^2 = 16 + 9 + 6*(-1) = 19 \Rightarrow B*C = \sqrt{19}
30,313
\sin(z) = \sin(z - \pi*2)
14,206
2 \cdot Cov[Q_1,Q_2]^2 = 2 \cdot (E[Q_1 \cdot Q_2] - E[Q_1] \cdot E[Q_2])^2 = 2 \cdot E[Q_1 \cdot Q_2]^2
36,976
0 = 2 + 2\times (-1)
11,406
bx + cx = (b + c) x
-11,764
\tfrac{1}{100} = (10^{-1})^2
-11,585
-12 + 8 i = i\cdot 8 - 10 + 2 \left(-1\right)
-27,507
3 \cdot x \cdot x = x \cdot x \cdot 3
-5,270
0.89*10^4 = 10^{7 + 3*(-1)}*0.89
7,299
\dfrac{3!}{(3 + 2\left(-1\right))!} = 3\cdot 2 = 6
44,835
\binom{3}{1}\binom{5}{2}\binom{2}{1}\binom{3}{2}\binom{1}{1}\binom{1}{1}\frac{3!}{2!}=540
-483
e^{\frac{19}{12} \cdot \pi \cdot i} \cdot (e^{i \cdot \pi \cdot 19/12})^2 = e^{\dfrac{19}{12} \cdot \pi \cdot i \cdot 3}
13,035
a \cdot c = a = c \cdot a
34,953
2^2 * 2 + 5^0 = 3 * 3
6,775
\frac{n}{n + 2} = -\dfrac{1}{2 + n}\cdot 2 + 1
18,471
\left(z*4 + 1\right)^{14}*15*4 = 60*(4*z + 1)^{14}
7,050
a*\phi_m*x = \phi_m*x*a
-22,912
112/140 = \frac{28\cdot 4}{28\cdot 5}
22,292
gf^5 gf = g^2 f^{11} = g^2 f^4
2,922
\frac{9^{20}}{10^{20}} \cdot 10 = \frac{1}{10^{19}} \cdot 9^{20}
23,228
Y = \sin{U \cdot \pi \cdot 2} \implies U = \dfrac{\operatorname{asin}(Y)}{\pi \cdot 2}
1,434
\cos\left(x + x \cdot 999\right) = \cos{x \cdot 1000}
17,240
c\cdot d\cdot 2 + c^2 + d^2 = \left(d + c\right)^2
4,592
n^2\cdot 4 + 7\cdot n + 3 = n^2\cdot 4 - n + n\cdot 8 + 3
4,925
2 + u_n\cdot 3 = u_{n + 1} \implies 1 + u_{n + 1} = 3 + 3\cdot u_n = 3\cdot (1 + u_n)
19,443
\frac{4}{216} \cdot 6 \cdot 5 = \frac19 \cdot 5
11,158
\left(1 + x \cdot x\right) (7 + x \cdot x + x) = x^4 + x^3 + x^2\cdot 8 + x + 7
-16,034
6*5*4 = \tfrac{1}{3!}6! = 120
-22,723
\frac{117}{78} = \dfrac{39}{2 \cdot 39} \cdot 3
7,883
\frac{1}{2^{1 + n}}\cdot (3\cdot (-1) + 2\cdot n + 4 - n) = \frac{1}{2^{1 + n}}\cdot \left(n + 1\right)
26,350
R_1 = X \cdot X \implies R_1^{1/2} = X
37,082
2*y^2 + 6*y + 4 = 2*(y * y + 3*y + 2) = 2*(y + 1)*(y + 2)
6,030
\dfrac{168^2}{h^2} + h^2 = 25 \cdot 25 \implies 168 \cdot 168 + h^4 = 25^2 h^2
-9,294
56\cdot (-1) - t\cdot 48 = -2\cdot 2\cdot 2\cdot 7 - 2\cdot 2\cdot 2\cdot 2\cdot 3\cdot t
-1,884
3/2\times \pi - \pi\times 7/4 = -\frac{\pi}{4}
-26,469
h^2 + 2 \cdot b \cdot h + b^2 = (h + b) \cdot (h + b)
-28,978
8={12}-4
7,113
\tfrac{\pi\cdot \left(z + (-1)\right)}{z \cdot z + (-1)} = \frac{\pi}{z + 1}
28,722
(F\cdot F^Q)^Q = (F^Q)^Q\cdot F^Q = F\cdot F^Q
-19,000
7/8 = \frac{1}{64 \cdot π} \cdot G_p \cdot 64 \cdot π = G_p
11,620
5 + 0*\sqrt{30} = (\sqrt{5})^2
31,383
4\cdot π^2\cdot R\cdot r = R\cdot π\cdot 2\cdot 2\cdot r\cdot π
25,522
(b + a)^2 = 2 \cdot a \cdot b + a^2 + b^2
-14,199
-\dfrac{1}{1 + 4 \left(-1\right)} 30 = -\frac{30}{-3} = -30/(-3) = 10
15,529
8\cdot x^2 + x\cdot 2 = 4\cdot x\cdot (x\cdot 4 + 1)/2
3,279
2^l = 1 + 2^0 + 2^1*...*2^{l + (-1)}
-19,356
7/3*\dfrac{1}{1}4 = \frac{7*\frac{1}{3}}{\frac{1}{4}}
17,458
\left(y + z\right)^2 = y^2 + z^2 + z y*2
18,405
6 = 2.3 = (1 + (-5)^{1/2}) \cdot (1 - (-5)^{1/2})
-341
\frac{6!}{\frac{1}{(9 + 3*(-1))!*3!}*9!}*\frac{1}{3!*(6 + 3*(-1))!} = 6!*\frac{1}{3!}/(9!*1/6!)
34,056
(z + 1)^{\frac{1}{3}} = (z + 1)^{\frac{1}{3}}
-20,824
\frac{1}{y*7 + 63}(y*28 + 42) = \frac{1}{9 + y}\left(6 + 4y\right) \dfrac{7}{7}
-29,456
3\cdot 9 + 6(-1) = 27 + 6(-1) = 21
1,556
\dfrac{n!}{r!*(-r + n)!} = \binom{n}{r}
9,751
\frac{n}{4} \cdot 3 = (n/2 + n)/2
23,898
x * x + (-1) = (x + (-1)) (1 + x)
34,851
y = m = 15 \implies y - m
-19,502
\frac{8\cdot \frac{1}{7}}{7\cdot 1/8} = \frac87\cdot \frac{8}{7}
25,547
1 - (\frac15*8)^{-\frac13} = -\frac{5^{1/3}}{2} + 1
39,116
\frac{1}{y \cdot z} = \frac{1}{y \cdot z}
8,665
\frac{dw}{dx}*v + \frac{dv}{dx}*w = \frac{\partial}{\partial x} \left(w*v\right)
8,533
(m + 1) \cdot (m + 2) = m \cdot m + 3 \cdot m + 2 > 2 \cdot m
42,082
\frac{\log_e\left(1\right)}{6} = 0