id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
6,148
|
\dfrac{x}{x \cdot \sqrt{(-1) + x^2}} = \frac{1}{\sqrt{(-1) + x^2}}
|
-3,589
|
3/4 \cdot \frac{x}{x^4} = \frac{3}{x^4 \cdot 4} \cdot x
|
21,454
|
\dfrac75 = 1 + \frac25 = 1 + \frac{1}{2 + \frac12}
|
-3,923
|
\frac{80}{t^3 \cdot 96} t^3 = \dfrac{80}{96} \dfrac{t^3}{t^3}
|
-4,734
|
\frac{13 + y\cdot 2}{4(-1) + y^2 + y\cdot 3} = -\frac{1}{y + 4} + \frac{3}{y + (-1)}
|
26,470
|
(-24*i + 7)^{1/2} = y rightarrow y^2 = 7 - i*24
|
-24,637
|
37 = 1 + 36
|
36,263
|
1 = -1^2*3 + 2^2
|
-11,978
|
\frac{1}{12}7 = \frac{p}{12 \pi}\cdot 12 \pi = p
|
31,961
|
(m + (-1)) \cdot m \cdot 2 + (m + (-1)) \cdot m = 3 \cdot m \cdot (m + (-1))
|
13,546
|
A_4 = \left\{3, 4, 1\right\}\Longrightarrow 3 = |A_4|
|
-22,374
|
6 + t^2 - t\cdot 7 = \left(6\cdot \left(-1\right) + t\right)\cdot (t + (-1))
|
8,320
|
\tfrac{\frac{1}{2}}{2} \cdot \frac12 = \frac{1}{8}
|
7,703
|
1 + n\cdot z + z = 1 + (n + 1)\cdot z \leq \left(1 + z\right)^n + z
|
20,069
|
98 = 100 + 3 \cdot \left(-1\right) + 1
|
-9,907
|
0.01 (-47) = -\tfrac{1}{100}47 = -0.47
|
-1,706
|
17/12\times \pi + \frac{17}{12}\times \pi = 17/6\times \pi
|
12,525
|
(-z + R)\cdot (z + R) = R^2 - z^2
|
19,832
|
g\cdot f/c = f\cdot g/c
|
2,263
|
3*\pi*|z| + 5 = |5 + |z|*\pi*3|
|
24,039
|
3145 \cdot 3145 = 2263 \cdot 2263 + 2184^2 = 1463^2 + 2784^2 = 336^2 + 3127^2
|
-1,922
|
\pi/2 + \pi\cdot \frac{19}{12} = 25/12\cdot \pi
|
11,723
|
\frac{1}{z + (-1)}\cdot \left(z + 1\right)\cdot (z + (-1)) = \frac{z + \left(-1\right)}{z + (-1)}\cdot (z + 1) = z + 1
|
33,761
|
E(W + Y) = E(W) + E(Y)
|
18,915
|
\dfrac{1}{4}\cdot 1/2/4 + \frac{9}{32} = 10/32
|
5,006
|
\frac{1}{24}*6 = 3/12
|
21,942
|
2\cdot n + 2\cdot m + 1 = 2\cdot (m + n) + 1
|
34,388
|
\tfrac{1}{1 + 1 + 1} = 1/3
|
36,212
|
0 = y^2 - 8 y + 48 (-1) = (y + 12 (-1)) (y + 4)
|
-29,360
|
(z + 3)*(z + 3*(-1)) = z^2 - 3^2 = z^2 + 9*\left(-1\right)
|
-5,316
|
10^{-2 + 4}\cdot 38.4 = 38.4\cdot 10^2
|
27,233
|
\frac{1}{4}*1/4/4 = \dfrac{1}{64}
|
20,732
|
X^2 \cdot X \cdot x = (X \cdot x^{1/3}) \cdot (X \cdot x^{1/3}) \cdot (X \cdot x^{1/3})
|
36,175
|
y \cdot \alpha + z \cdot \alpha = \alpha \cdot \left(z + y\right)
|
-7,351
|
\frac{1}{7}5\cdot 6/8\cdot 4/6 = 5/14
|
21,320
|
y\cdot Y = y\cdot Y
|
2,520
|
\left(-z^2 + 1 = Q \Rightarrow z^2 = 1 - Q\right) \Rightarrow z = \sqrt{1 - Q}
|
-9,242
|
3*3*5*q - 3*3*13 = q*45 + 117*(-1)
|
34,317
|
200 \times (-1) + 140 + 120 = 60
|
1,293
|
z \cdot z \cdot z + h^2 \cdot h + f^3 = z^3 + h \cdot h \cdot h + f \cdot f^2 - 3 \cdot f \cdot h \cdot z + 3 \cdot f \cdot h \cdot z
|
24,189
|
u^{\frac12} = (u^{1/4})^2
|
37,499
|
3^2 = 2^2 + 5^1
|
-428
|
-8\cdot \pi + \pi\cdot 115/12 = \frac{1}{12}\cdot 19\cdot \pi
|
26,497
|
2 = \sqrt{2} \cdot \sqrt{2} = (2^{1/4})^4 = \ldots
|
-20,523
|
\tfrac{5}{5} \cdot \frac{1}{x \cdot (-10)} \cdot (9 - 8 \cdot x) = \tfrac{45 - x \cdot 40}{(-50) \cdot x}
|
17,747
|
\frac{1}{A A^T} = \frac{1}{A^T A}
|
-7,587
|
\dfrac{-8}{-4i} + \dfrac{12i}{-4i} = \dfrac 1i \left(\dfrac{-8}{-4} + \dfrac{12i}{-4} \right)= \dfrac 1i (2-3i)
|
4,186
|
z_k\cdot z_n = z_k\cdot z_n
|
12,245
|
\frac{1}{2} = \frac34 \cdot \tfrac{2}{3} + \dfrac{1}{4} \cdot 0
|
34,432
|
\frac{x + a}{x - a} = \dfrac{\frac1x \cdot a + 1}{1 - \frac{a}{x}}
|
7,629
|
d + (-1) = \dfrac12\cdot (d + (-1)) + (d + (-1))/2
|
9,081
|
3! {5 \choose 3} {5 \choose 3}*2 = 1200
|
-3,107
|
\sqrt{4 \cdot 2} + \sqrt{16 \cdot 2} - \sqrt{9 \cdot 2} = \sqrt{8} + \sqrt{32} - \sqrt{18}
|
2,848
|
\cos(\frac{\pi}{2} \cdot (x + 2 \cdot \left(-1\right))) = \cos(\frac{\pi}{2} \cdot x - \pi) = -\cos(\dfrac12 \cdot \pi \cdot x)
|
-9,003
|
74\% = \dfrac{74}{100}
|
-7,407
|
8/15 = 4/5\times \frac{2}{3}
|
4,910
|
\frac{x + \left(-1\right)}{x + 1} = 1 - \frac{2}{x + 1}
|
-8,008
|
\tfrac{1}{32} \cdot (-32 + 96 \cdot i - 32 \cdot i + 96 \cdot (-1)) = \frac{1}{32} \cdot (-128 + 64 \cdot i) = -4 + 2 \cdot i
|
-4,157
|
\frac{1}{35}63 \dfrac{1}{y^5}y^3 = \frac{y^3}{35 y^5}63
|
-1,526
|
-\frac74*\frac19*5 = \dfrac{1}{\frac{1}{5}*9}*\left((-7)*\dfrac14\right)
|
7,427
|
x^2 = 9 \cdot x^2 + 6 \cdot x + 1 = 3 \cdot (x^2 + 2 \cdot x) + 1
|
-18,964
|
\frac35 = \frac{x_t}{4\cdot \pi}\cdot 4\cdot \pi = x_t
|
51,082
|
d + x^3 - x^2*(\alpha + C + \gamma) + x*(\alpha*C + \gamma*C + \alpha*\gamma) - C*\gamma*\alpha = (-C + x)*(x - \gamma)*(-\alpha + x) + d
|
9,202
|
100 - 20\cdot x + x \cdot x = (-x\cdot 2 + 10)\cdot 10 + x^2
|
-16,331
|
i = 4 b = b + 24
|
10,281
|
\frac{cch}{c^2} = c\frac1ch
|
7,270
|
\frac{29}{32} = -(1/2 + \frac14)\cdot \tfrac{1/2}{2}/2 + 1
|
10,232
|
23 = 10^0 \cdot 3 + 2 \cdot 10^1
|
32,923
|
1.6 = 0.16 + 1.5*0.48 + 2*0.36
|
6,058
|
\mathbb{E}[V \times V] = \mathbb{Var}[V] + \mathbb{E}[V]^2
|
-20,451
|
\frac{1}{10 + r}*\left(9*(-1) + r*9\right)*6/6 = \dfrac{1}{60 + 6*r}*(54*r + 54*(-1))
|
-3,932
|
\frac{1}{11\cdot r}\cdot 3 = 1/11\cdot 3/r
|
-28,789
|
\int x \cdot x^2\,dx = \frac{1}{3 + 1}\cdot x^{3 + 1} + Y = \frac{x^4}{4} + Y
|
15,217
|
\cos(y + z) = -\sin(z) \cdot \sin(y) + \cos(z) \cdot \cos(y)
|
-7,002
|
4/7 \cdot \dfrac58 \cdot \frac36 = \dfrac{5}{28}
|
28,604
|
\frac{1}{945}\cdot 1689 = \frac{1}{9} + 1 + \frac{1}{3} + \frac15 + 1/7
|
19,695
|
r \times x^{(-1) + r} = \frac{\partial}{\partial x} x^r
|
-10,495
|
-\dfrac{41}{48} = -41/48
|
6,066
|
\sin(x) = \tfrac{15}{17} rightarrow 8/17 = \cos(x)
|
25,602
|
\left(2 + 3^{1/2}\right)^4 + (-3^{1/2} + 2)^4 = 194
|
16,720
|
\tfrac{13}{21} + 1 = 34/21
|
30,959
|
2 + y \cdot y - 2\cdot y = 1 + ((-1) + y)^2
|
-24,848
|
\int \dfrac{1}{x^2}\,dx = \frac{1}{x*(-2 + 1)} + C = -1/x + C
|
6,390
|
5 + \text{i}\cdot 12 = (3 + 2\cdot \text{i}) \cdot (3 + 2\cdot \text{i})
|
31,107
|
\dfrac{2/3}{2} + 1/3 = 2/3
|
-20,325
|
-40/8 = \frac18\cdot 8\cdot (-\dfrac{1}{1}\cdot 5)
|
21,235
|
100! = 99*97*95!*96*98*100
|
-593
|
\pi\cdot \frac16\cdot 11 = \pi\cdot 35/6 - 4\cdot \pi
|
15,103
|
(x^{1/4})^4 = (x^{\frac13\cdot 4})^{3/4} = |x|
|
19,138
|
(-1) + p = r + \left(-1\right)\Longrightarrow r = p
|
20,335
|
1/x = Z_2*Z_1 \implies \tfrac{1}{x*Z_1} = Z_2
|
14,710
|
\left(y^Z\cdot L\cdot y\right)^Z = y^Z\cdot L^Z\cdot y = -y^Z\cdot L\cdot y
|
10,371
|
h\cdot a = -a\cdot (-h)
|
14,980
|
\frac{\partial}{\partial x} (\frac1x \cdot b) = b \cdot \frac{d}{dx} \dfrac{1}{x}
|
5,889
|
\frac{3}{2}\cdot \pi = \pi\cdot 2 + (\pi\cdot (-1))/2
|
4,645
|
a! \cdot \frac{1}{a!} \cdot b! + a! = (1 + b!/a!) \cdot a!
|
16,477
|
m\cdot n/g = \frac{m}{g}\cdot n = m\cdot n/g
|
37,083
|
17^2 + (-1) = 288 = 24\cdot 12
|
-26,469
|
(a + b)^2 = b^2 + a^2 + a*b*2
|
3,803
|
r \cdot r^2 \cdot z = r^3 \cdot z
|
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