id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
-4,814
|
1.8/1000 = \dfrac{1}{1000}1.8
|
-25,510
|
\frac{d}{dx} (\frac{1}{2 + x} 4) = -\frac{1}{\left(2 + x\right)^2} 4
|
31,873
|
\cos{x} + \sin{x} = Y \cdot \sin(x + x_0) = Y \cdot \sin{x} \cdot \cos{x_0} + Y \cdot \cos{x} \cdot \sin{x_0}
|
23,589
|
\left(S + 2 \times (-1)\right) \times 2^n = 0 = (S + 1) \times (-1^n)
|
21,659
|
h\cdot h + g\cdot h + h\cdot g + g\cdot g = (h + g)^2
|
5,670
|
2\cdot b \cdot b - b\cdot 2 + (-1) = 0\Longrightarrow b = \frac12\cdot (1 \pm 3^{1/2})
|
12,437
|
(-1)^{1/n} = \left(e^{\pi\cdot i}\right)^{\frac{1}{n}} = e^{\pi\cdot i/n}
|
494
|
z^3 - \gamma^3 = (z^2 + \gamma\cdot z + \gamma^2)\cdot (z - \gamma)
|
-19,626
|
\frac{1}{3}*8/(7*1/5) = 5/7*\frac{8}{3}
|
34,091
|
\dfrac{x}{y} = 1/\left(\frac1x y\right)
|
-6,628
|
\frac{3}{5 \cdot (n + 4)} = \tfrac{3}{n \cdot 5 + 20}
|
7,356
|
z^4 \cdot 7 + 4 \cdot z^3 + z^2 \cdot 8 + 11 \cdot z - z^4 \cdot 7 - 3 \cdot z \cdot z \cdot 2 - 2 \cdot (z \cdot 5 + 2 \cdot z^3 + z \cdot z) = z
|
35,924
|
2*z*y^2*z*2 = y * y*z^2*4
|
20,821
|
a a - b b = (a - b) (a + b)
|
-1,810
|
-\frac{1}{6}\pi + \frac{\pi}{6} = 0
|
10,823
|
2100/9 = 700/3 = 699/3 + \frac13 = 233 + \dfrac{1}{3}
|
-742
|
(e^{\frac{11}{6} \times \pi \times i})^{11} = e^{\dfrac{1}{6} \times \pi \times 11 \times i \times 11}
|
-5,619
|
\frac{1}{(6\cdot (-1) + y)\cdot (y + 5)}\cdot 2 = \frac{2}{30\cdot \left(-1\right) + y^2 - y}
|
-20,978
|
\dfrac{15 - 12\times x}{-21\times x + 12} = 3/3\times \tfrac{-4\times x + 5}{-7\times x + 4}
|
-7,298
|
\frac27\cdot 0 = 0
|
-471
|
(e^{\frac{5}{12} \cdot \pi \cdot i})^{12} = e^{\dfrac{5}{12} \cdot \pi \cdot i \cdot 12}
|
13,388
|
(1 + l)^2 = 1 + l \cdot l + 2\cdot l
|
37,797
|
2 \cdot z + x - z = z + x
|
-20,953
|
\dfrac{64}{s\cdot 40}\cdot s = \frac{8}{5}\cdot s\cdot 8/(8\cdot s)
|
12,661
|
(b + c) a = ac + ba
|
19,325
|
(1/4)^2 + (1/2)^2 + (1/4) \cdot (1/4) = \frac{3}{8} = 0.375
|
-10,266
|
\frac{3}{3} (-\frac{4}{5x + 10}) = -\frac{12}{30 + 15 x}
|
-1,581
|
\dfrac{23}{12} \pi + \pi/6 = \pi \cdot 25/12
|
960
|
\dfrac{2101}{3125} = 1 - (\frac154)^5
|
6,398
|
\binom{2}{0}\times \binom{2}{1}\times \binom{4}{1} = 8
|
17,935
|
25 + 20 \cdot \left(-1\right) = 5
|
8,719
|
150 = 5!/(2!*3!) \binom{6}{4}
|
-12,344
|
\sqrt{7} \cdot 3 = \sqrt{63}
|
-9,269
|
y*y*2*2 + y*y*2*2*y = 4*y^2 + y^3*4
|
-21,059
|
2/4 = \frac48
|
-20,160
|
\dfrac{24}{-12 x + 36 (-1)} = \frac{6}{-x \cdot 3 + 9 (-1)} \frac{4}{4}
|
8,184
|
\frac{1}{p! \times \left(-p + n\right)!} \times n! = \binom{n}{p}
|
7,329
|
d^2*I_k + I_k*x^2 = I_k*(d^2 + x^2)
|
21,322
|
3 = 11 - 4k \Rightarrow 2 = k
|
14,844
|
27 + D \cdot 26 + x = 26 \cdot (1 + D) + x + 1
|
8,406
|
\left(\frac{y}{b}\right)^2 = (y/b)^2
|
-11,962
|
2/5 = s/\left(4\pi\right)*4\pi = s
|
14,209
|
\dfrac{2}{2^n} = \frac{1}{2^{n + \left(-1\right)}}
|
-22,288
|
(1 + r)\cdot \left(9 + r\right) = 9 + r^2 + 10\cdot r
|
-17,690
|
38\cdot \left(-1\right) + 56 = 18
|
8,694
|
z^{2^{n + 1}} = (z^{2^n})^2
|
20,345
|
y \cdot y - 2 \cdot y + 3 \cdot \left(-1\right) = (y + 1) \cdot (y + 3 \cdot (-1))
|
-20,745
|
\dfrac{1}{-8} \cdot (5 - 10 \cdot x) \cdot \dfrac{9}{9} = (-90 \cdot x + 45)/(-72)
|
3,693
|
10 = 4l \implies \frac52 = l
|
18,224
|
\left\lfloor{\frac{1}{4} \cdot (300/3 + 2)^2}\right\rfloor = 2601
|
-2,184
|
\frac{3}{11} - 2/11 = \frac{1}{11}
|
25,964
|
108124016 = \left(2002\cdot (-1) + 15504\right)\cdot (6006 + 2002)
|
4,981
|
{5 \choose 2} {5 \choose 3} = 100
|
42,468
|
2^4 + 3^2 = 5^2
|
8,888
|
(-1) + n^2 = \left(n + 1\right) \left(n + (-1)\right)
|
4,608
|
x - N + (-1) = x - N + 1
|
-12,593
|
3 = \dfrac{31.5}{10.5}
|
8,257
|
x \cdot x + x \cdot 2 - -7 \cdot x + x^2 = 9 \cdot x
|
-9,529
|
27 = 3\cdot 9
|
27,048
|
12/17\cdot 2/3 = \frac{8}{17}
|
12,228
|
x^2 + 2*y^2 + B^2 + 2*y^2 = x^2 + 4*y^2 + B^2
|
6,186
|
c^{\dfrac{1}{2}\cdot 3}/(\frac1c) = c^{3/2}\cdot c = c^{5/2}
|
-4,464
|
20 \cdot (-1) + Y^2 - Y = (Y + 4) \cdot (Y + 5 \cdot (-1))
|
1,747
|
\left(3 + n\right) \cdot (\left(-1\right) + n) = n \cdot n + n \cdot 2 + 3 \cdot \left(-1\right)
|
16,182
|
\sin(1 + m) = \sin(m) \cos\left(1\right) + \sin\left(1\right) \cos(m)
|
26,801
|
8315 = 21 \times 21 \times 5 \times 3 + 5^2 \times 21 \times 3 + 5^3
|
-555
|
\dfrac{1}{12} \pi = 169/12 \pi - \pi*14
|
33,703
|
1 = \sin(\theta) \implies \theta = \pi/2
|
31,822
|
-(m^2 + (-1)) + m^2 \cdot 2 = m^2 + 1
|
18,173
|
x^2 = ((-1) + x)^2 + x\cdot 2 + (-1)
|
34,442
|
\sqrt{-1 + \sqrt{2}\cdot 2} = \sqrt{2\cdot \sqrt{2} - 1}
|
29,746
|
\frac{1}{z^2}(C_1 + zC_2) = \frac{C_2}{z} + \frac{C_1}{z^2}
|
20,018
|
1/60 = \dfrac18\cdot (\dfrac13 - 1/5)
|
32,141
|
4\times 3! = 24
|
43,577
|
-3\cdot 4 + 48 = 36
|
-7,732
|
\left(40 + 16 \cdot i + 100 \cdot i + 40 \cdot (-1)\right)/29 = \tfrac{1}{29} \cdot (0 + 116 \cdot i) = 4 \cdot i
|
13,522
|
0 = Iy \Rightarrow I = 0\text{ or }y = 0
|
1,698
|
\sin(H + B) = \cos(B) \cdot \sin(H) + \sin(B) \cdot \cos(H)
|
15,111
|
( x, B*y*\Phi(f)) = ( x, y*B*\Phi(f))
|
1,936
|
\pi\cdot 3/2 + \cos{\dfrac{3}{2}\cdot \pi} = y + 1 \Rightarrow 2\cdot (-1) + \pi\cdot 3/2 = y
|
2,703
|
\left(z + 5 \cdot (-1) \geq 0 \Rightarrow z + 5 \cdot (-1) = 1\right) \Rightarrow z = 6
|
43,809
|
965 = 5 \cdot 193
|
12,661
|
ha + ag = a\cdot (g + h)
|
27,463
|
1260 = 2 \cdot 2\cdot 3 \cdot 3\cdot 5\cdot 7
|
1,052
|
(a + g)\times (a \times a - a\times g + g^2) = a^3 - a^2\times g + a\times g^2 + a \times a\times g - a\times g^2 + g^3 = a \times a \times a + g^3
|
8,149
|
2 + 2*z = 2*\left(z + 1\right)
|
37,383
|
P(x) = X^x\cdot B = B\cdot X^x
|
30,608
|
47 = 2*(-1) + (1 + 2*3) * (1 + 2*3)
|
-29,563
|
\dfrac{1}{z} \cdot (2 \cdot \left(-1\right) + 3 \cdot z^3 - z) = -2/z + \frac{3}{z} \cdot z^3 - z/z
|
30,849
|
2\cdot (-1) + n = -\left(3 + (-1)\right) + n
|
13,108
|
0 = T * T - \lambda * \lambda = \left(T - \lambda\right)*(T + \lambda) = (T - \lambda)*\left(T - -\lambda\right)
|
32,148
|
\infty + 2(-1) = \infty
|
5,993
|
\left(-x_0^{1/2} + x^{1/2}\right) (x_0^{1/2} + x^{1/2}) = x - x_0
|
-27,416
|
667 + 10 = 677
|
5,223
|
(a \times b)^2 = (b \times a)^2
|
-5,159
|
0.81\cdot 10^{6 + 2\cdot (-1)} = 0.81\cdot 10^4
|
31,498
|
(g \cdot g + a^2 + g\cdot a)\cdot 4 = \left(g + 2\cdot a\right)^2 + 3\cdot g^2
|
-10,630
|
\frac{25}{t\times 15} = 5/5\times \frac{5}{t\times 3}
|
-7,967
|
(-21 + 72 \cdot i + 28 \cdot i + 96)/25 = (75 + 100 \cdot i)/25 = 3 + 4 \cdot i
|
11,942
|
(A+B)x = 0 \implies Ax + Bx = 0
|
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