id
int64 -30,985
55.9k
| text
stringlengths 5
437k
|
|---|---|
11,620
|
5 + \sqrt{30} \cdot 0 = \sqrt{5} \cdot \sqrt{5}
|
-1,035
|
2 * 2 = 2*2 = 4
|
-1,727
|
-\pi*\frac56 = -\frac76*\pi + \frac{1}{3}*\pi
|
-16,797
|
7 = 7\cdot 5\cdot k + 7\cdot 4 = 35\cdot k + 28 = 35\cdot k + 28
|
-27,485
|
11\cdot c\cdot c\cdot c\cdot 2 = c^3\cdot 22
|
-18,083
|
31 = 17 \cdot (-1) + 48
|
49,613
|
\frac{1}{-x + 3} \cdot (3/2 + \frac12 \cdot 3 \cdot x) = -\frac12 \cdot 3 + \dfrac{2}{-\dfrac{x}{3} + 1}
|
-10,622
|
\frac{15*(-1) + x*15}{36 + 24*x} = \frac{5*(-1) + x*5}{12 + x*8}*3/3
|
11,621
|
0 = z^4 + 6*z^2 + 25 = (z^2 + 5)^2 - 4*z^2 = (z * z - 2*z + 5)*(z^2 + 2*z + 5)
|
14,621
|
-7 \cdot 17 + 2 \cdot 60 = 17 \cdot (-1) + 2 \cdot \left(-17 \cdot 3 + 60\right)
|
12,348
|
x + y \cdot 0.5 = 1.75 \Rightarrow x = 1.75 - y \cdot 0.5
|
24,209
|
z^{1 + k} = z^k \cdot z
|
27,985
|
|z + (-1)| = |1 - z| \geq |1| - |z| = 1 - |z| \Rightarrow |z| \geq \frac{1}{4} \cdot 3
|
9,336
|
\left(\left(2 = a + 1/a \Rightarrow 0 = a^2 - 2\cdot a + 1\right) \Rightarrow \left(a + (-1)\right) \cdot \left(a + (-1)\right) = 0\right) \Rightarrow 1 = a
|
19,830
|
X \backslash E + z = X \cap \overline{E + z} = X \cap \overline{E} + z
|
23,311
|
\left(1 + 2 rightarrow k_1 \cos(E) + k_2 \sin(E) = 1\right) rightarrow \left(\cos(E) k_1\right)^2 = (-\sin(E) k_2 + 1)^2
|
14,676
|
45*(-1) + 25 = 36*(-1) + 16
|
8,699
|
(a \cdot x) \cdot (a \cdot x) = (x \cdot a) \cdot (x \cdot a)
|
-29,195
|
-1 \cdot 2 + 4\cdot 1 = 2
|
3,037
|
\tfrac{\sin{x^5}}{x^5}*x^4 = \frac{\sin{x^5}}{x}
|
12,956
|
1 - \frac{2 \cdot c}{a - b + c} \cdot 1 = \frac{1}{a - b + c} \cdot (-c \cdot 2 + a - b + c)
|
6,189
|
128\times 512 = 2^7\times 2^9 = 2^{16} = 65536
|
-20,980
|
\frac{90 (-1) - s*9}{10 s + 100} = \frac{10 + s}{s + 10} (-\frac{9}{10})
|
-2,660
|
\sqrt{11} \cdot 4 + \sqrt{11} = \sqrt{16} \cdot \sqrt{11} + \sqrt{11}
|
-26,907
|
\sum_{x=1}^∞ \frac{(-5)^x}{x\cdot 5^x} = \sum_{x=1}^∞ \frac{(-1)^x\cdot 5^x}{x\cdot 5^x} = \sum_{x=1}^∞ (-1)^x/x
|
24,056
|
\tfrac{1}{\frac13 + 1/4} = \frac{12}{7}
|
14,552
|
\frac{2 + 2\cdot \sin(X)}{\cos(X)\cdot (1 + \sin(X))} = 2/\cos(X) = 2\cdot \sec(X)
|
41,730
|
4 + 6\times 166 = 1000
|
15,997
|
A - C = 0 \Rightarrow -C^2 + A^2 = 0
|
36,996
|
|g\cdot x| = |g\cdot x|
|
6,677
|
9 \cdot (-1) + 2 \cdot d = 2 \cdot d + 1 + 10 \cdot (-1)
|
-5,246
|
1.35 \times 10 = \frac{13.5}{10^6} \times 1 = \dfrac{1.35}{10^5}
|
33,927
|
2 \cdot \left(c - x\right) = -(x - c) + c - x
|
34,883
|
(y + h)\cdot \overline{y + h} = y\cdot \bar{y} + y\cdot \bar{h} + \bar{y}\cdot h + h\cdot \bar{h} = |y|^2 + 2\cdot \operatorname{re}{(y\cdot \bar{h})} + |h|^2
|
-11,886
|
1.255/10 = 1.255\cdot 0.1
|
8,295
|
\sqrt{6 + \sqrt{20}} = \sqrt{6 + 2\cdot \sqrt{5}}
|
-22,769
|
\frac{70}{30} = \frac{10}{10 \cdot 3} \cdot 7
|
7,466
|
\sin(\pi*4 + \pi*2) = \sin{\pi*4} + \sin{2\pi}
|
-23,180
|
-6 = -1/2 \times 12
|
-20,934
|
\dfrac{-r \cdot 7 + 2}{2 - r \cdot 7} (-1^{-1}) = \frac{2(-1) + 7r}{2 - 7r}
|
9,365
|
\frac{z + 1}{z + (-1)} = \frac{1}{\left(z + (-1)\right) \cdot 1/z} \cdot \tfrac{1}{z} \cdot (z + 1) = \frac{1 + 1/z}{1 - 1/z}
|
31,311
|
x f_1 f_2 x = x f_1 f_2 x
|
52,345
|
100 \cdot 10.233 = \left\{1023.3\right\} = 0.3
|
50,596
|
7^1 = 2^1 + 5^1
|
-3,354
|
\sqrt{13}*(3 + 2 + 4) = \sqrt{13}*9
|
28,778
|
2*3*k + 5 = 2*3*k + 4 + 1 = 2*(3*k + 2) + 1
|
1,247
|
z + \left(-1\right) = I\Longrightarrow 1 + I = z
|
3,101
|
x\cdot K = 1/(x\cdot K) = 1/\left(K\cdot x\right) = K\cdot x
|
35,846
|
1 + e^{2i} = 1 + e^{i} \cdot e^{i} = 1 + e^i \cdot i \sin(1) + e^i \cdot \cos(1)
|
15,023
|
\frac{1}{x^2 - y^2} \cdot (x - y) = \frac{1}{y + x}
|
6,562
|
g^3 - b^3 = (g^2 + b\cdot g + b^2)\cdot (g - b)
|
4,185
|
(1 - \frac{1}{2})^{-\tfrac{3}{2}} = 2^{\frac12\cdot 3} = \sqrt{8}
|
15,680
|
\dfrac{\sin^r(\|x\|)}{\|x\|^r} \|x\|^{r + (-1)} = \frac{1}{\|x\|}\sin^r(\|x\|)
|
29,362
|
t + 3 = \dfrac{1}{3\cdot (-1) + t}\cdot \left(t^2 + 9\cdot \left(-1\right)\right)
|
-18,943
|
\frac{5}{6} = \frac{1}{9 \cdot \pi} \cdot A_s \cdot 9 \cdot \pi = A_s
|
8,512
|
a x + x b = (a + b) x
|
27,938
|
\sqrt{h} = h^{\frac{1}{2}}
|
21,836
|
2*27 + 9\left(-1\right) = 45
|
-18,803
|
\frac{5}{5} \cdot y = y
|
-4,410
|
z^2 + 3*z + 4*(-1) = (z + (-1))*(z + 4)
|
16,306
|
|A - y\cdot I| = |(A - y\cdot I)^Z| = |A^Z - y\cdot I|
|
16,174
|
A^2 - Z^2 = (A - Z) \cdot (A + Z)
|
18,087
|
(e + \left(-1\right)) \cdot ((-1) + g) = 70 \implies \left[g, e\right] = [2, 71], \left[3, 36\right], \left[6,15\right]
|
-15,100
|
\frac{1}{r^4*\frac{1}{k^{16}}}*k^4 = \frac{k^4}{\tfrac{1}{\frac{1}{r^4}*k^{16}}}
|
-6,468
|
\frac{3}{16 + z \cdot 2} = \frac{1}{\left(z + 8\right) \cdot 2} \cdot 3
|
1,287
|
\frac{1}{-61^3 + 1049^3}(1823^3 - 1699^3) = 1
|
31,553
|
(6 + 7 + 12 + 15 + 19)^3 = 19^4 + 6^4 + 7^4 + 12^4 + 15^4
|
6,298
|
2 \cdot \dfrac26 \cdot 3 \cdot \frac{6 + 3 \cdot (-1)}{6 + (-1)} = \frac15 \cdot 6 = 1.2
|
3,829
|
t - x + (-1) = t - x + 1
|
1,004
|
\frac{1}{1 - y^2} = \frac{1}{2 (y + 1)} + \frac{1}{2*(-y + 1)}
|
11,664
|
F * F^2 + 3F^2 H + 3H^2 F + H * H^2 = (H + F)^3
|
20,330
|
r^0 - r^l = 1 - r^l
|
3,314
|
\beta \cdot s - s^2 = -(s - \frac{\beta}{2}) \cdot (s - \frac{\beta}{2}) + \frac14 \cdot \beta \cdot \beta
|
11,242
|
\tfrac{9}{48} + 3/54 = 3/16 + 1/18 = \dots
|
4,392
|
(-b^2 + c * c)*x = x*(c - b)*\left(c + b\right)
|
-6,086
|
\frac{1}{40 + x*4}*5 = \frac{1}{(10 + x)*4}*5
|
2,230
|
0 = (g + b - d)\cdot z \cdot z + 2\cdot (g + b)\cdot z + g + b + d = (g + b)\cdot \left(z + 1\right) \cdot \left(z + 1\right) - d\cdot (z^2 + (-1))
|
-22,272
|
a^2 + 2 \times a + 15 \times (-1) = (a + 3 \times (-1)) \times (a + 5)
|
15,573
|
\dfrac{2 + 7}{1 + 3} = 9/4
|
13,517
|
\alpha^9\times \alpha\times \alpha^3 = \alpha^{13}
|
-2,771
|
(4 + 1)\cdot 5^{1 / 2} = 5\cdot 5^{1 / 2}
|
14,690
|
-10 \cdot x = 1 \pm \left(4 \cdot x^4 - 4 \cdot x^2 + 1\right)^{1/2} = 1 \pm ((2 \cdot x^2 + (-1)) \cdot (2 \cdot x^2 + (-1)))^{1/2}
|
11,781
|
84\cdot 256^3 + 101\cdot 256^2 + 256^1\cdot 115 + 256^0\cdot 116 = 1415934836
|
29,522
|
\frac{1}{\left(y - a\right) (y - b)} = \frac{1}{b - a}\left(-\frac{1}{y - a} + \dfrac{1}{-b + y}\right)
|
1,033
|
n = \dfrac12\cdot \left((-1) + 1 + 2\cdot n\right)
|
25,923
|
a^{b \cdot \psi} = (a^b)^\psi = (a^\psi)^b
|
-14,236
|
\dfrac{12}{9 + 3} = \tfrac{12}{12} = 12/12 = 1
|
-10,376
|
-12 = -2*y + 12 + 10*(-1) = -2*y + 2
|
41,768
|
\sum_{n=1}^\infty nx^{n-1}=\sum_{n=0}^\infty(n+1)x^n=\sum_{n=0}^\infty nx^n+\sum_{n=0}^\infty x^n
|
21,165
|
\left(\tfrac1x\right)^{1/5} = (\frac{1}{x})^{1/5} = x^{-1/5}
|
2,736
|
0 + 2 = C\Longrightarrow C = 2
|
8,159
|
3 = (\dfrac{1}{2}*\sqrt{12})^2
|
15,574
|
(b + a)^2 = a \cdot a + 2 \cdot a \cdot b + b^2
|
31,627
|
t*x^2/y = \frac{\left(t*x\right)^2}{y*t}
|
6,875
|
(O_l)/(\pi_l) = O_l/(\pi_l)
|
12,360
|
(k + 1)^3 - k + 1 - k^3 + k = k\cdot 3 + k^2\cdot 3
|
16,801
|
3*3*4*4=144
|
36,509
|
55 = 5^2 + 1 \times 1 + 2^2 + 3 \times 3 + 4^2
|
26,708
|
2^{\frac34} = \left(2^3\right)^{1/4}
|
7,139
|
\frac{\sqrt{1 + x^2} + x}{\sqrt{1 + x^2}} = 1 + \frac{x}{\sqrt{x^2 + 1}}
|
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