id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
23,677
|
x^2 - 12*x + 27 = 0 = \left(x + 3*(-1)\right)*(x + 9*(-1))
|
-11,744
|
1/9 = (\dfrac{1}{3})^2
|
14,796
|
e^m = \sum_{l=0}^\infty \frac{m^l}{l!} \gt \frac{1}{l!}\cdot m^l
|
38,810
|
h = 15 \cdot h \cdot x = 1.2 \cdot h \cdot x
|
7,140
|
5/1 = 5*\frac16/(1/6)
|
52,504
|
\sum_{n=1}^{2^{l_2} + (-1)} \frac{1}{n^p} = \sum_{n=2^{l_1}}^{2^{l_1 + 1} + (-1)} \frac{1}{n^p} < \sum_{n=2^{l_1}}^{2^{l_1 + 1} + (-1)} \frac{1}{(2^{l_1})^p}
|
-4,268
|
\dfrac{b^4}{b \cdot b \cdot b} = \frac{b^4}{b\cdot b\cdot b}\cdot 1 = b
|
-3,297
|
\sqrt{7}\cdot \sqrt{9} + \sqrt{7}\cdot \sqrt{16} - \sqrt{7}\cdot \sqrt{25} = 3\cdot \sqrt{7} + 4\cdot \sqrt{7} - \sqrt{7}\cdot 5
|
21,811
|
2(g + \beta) = \beta + g + \beta + g
|
-2,889
|
\sqrt{11} \times (5 + 2 \times \left(-1\right)) = 3 \times \sqrt{11}
|
-28,758
|
\frac{1}{3} - \frac{4}{3 \cdot y + 6} = \frac{1}{3} - \frac{\frac{4}{3}}{y + 2} \cdot 1
|
34,579
|
(a\cdot d)^i = \left(a\cdot d\right)^i
|
-15,885
|
4/10 \times 5 - 8 \times \frac{1}{10} \times 6 = -28/10
|
12,072
|
e^{-x} = -6*x \Rightarrow \frac{1}{e^x} = -6*x
|
34,226
|
\frac{1}{1 + b}\times b = \frac{1 + b + (-1)}{1 + b} = 1 - \dfrac{1}{1 + b}
|
-22,291
|
z^2 - z*11 + 18 = (z + 2(-1)) (z + 9(-1))
|
-2,538
|
10*7^{1/2} = (4 + 1 + 5)*7^{1/2}
|
-18,472
|
\dfrac{36}{21} = 12/7
|
-7,162
|
3/22 = \frac{1}{11} \cdot 3 \cdot \frac{1}{12} \cdot 6
|
-26,414
|
-12/5 (-2) = \dfrac15 24
|
-9,411
|
-2\cdot 2\cdot 3\cdot 7 + z\cdot 2\cdot 2\cdot 2\cdot 3\cdot 5 = z\cdot 120 + 84\cdot (-1)
|
-13,855
|
9 - 1 \cdot 2 + 8/8 = 9 - 1 \cdot 2 + 1 = 9 + 2 \cdot (-1) + 1 = 7 + 1 = 8
|
-4,511
|
-\frac{2}{y + 5 \cdot (-1)} + \frac{4}{y + (-1)} = \dfrac{1}{5 + y^2 - y \cdot 6} \cdot \left(y \cdot 2 + 18 \cdot \left(-1\right)\right)
|
-5,902
|
\frac{4}{(r + 8)\cdot (r + 4\cdot (-1))} = \frac{1}{32\cdot (-1) + r^2 + r\cdot 4}\cdot 4
|
18,974
|
|z - \frac{1}{2}(z + y)|^2 = |\frac{z}{2} - y/2|^2 = |\frac{1}{2}(z + y) - y|^2
|
10,215
|
\frac{\frac{1}{100}}{2} \cdot 20 = \frac{1}{5 \cdot 2} = \frac{1}{10}
|
16,933
|
\Omega^{-1}=\Omega^{-1/2}\Omega^{-1/2}
|
14,449
|
(-1) + 4\cdot x = 0 \Rightarrow \frac{1}{4} = x
|
11,807
|
f_2 \cdot f_2 + f_1 \cdot f_1 + f_2^2 \cdot f_1^2 = (f_2 - f_1)^2 + 2 \cdot f_2 \cdot f_1 + f_2^2 \cdot f_1^2 = 1 + 2 \cdot f_2 \cdot f_1 + f_2^2 \cdot f_1 \cdot f_1 = (1 + f_2 \cdot f_1)^2
|
38,826
|
{10 \choose 3}*{7 \choose 2}*{5 \choose 2}*3! = 10!/(7!*3!)*\dfrac{1}{5!*2!}*7!*5!/(3!*2!)*3! = \frac{10!}{3!*2!*2!}
|
8,605
|
1/(1/(g_2) g_1) = g_2/(g_1)
|
-5,112
|
10^{(-2)\cdot (-1) + 0}\cdot 0.93 = 0.93\cdot 10^2
|
33,148
|
-1 - e^{-2 \times i} = -(1 + e^{-2 \times i})
|
19,554
|
(y^2 + 4\cdot (-1))^{1 / 2} - y = \frac{y^2 + 4\cdot \left(-1\right) - y^2}{(y^2 + 4\cdot (-1))^{\tfrac{1}{2}} + y} = -\frac{4}{(y^2 + 4\cdot (-1))^{1 / 2} + y}
|
23,134
|
\cos(\pi + \pi \cdot z) = -\cos(\pi \cdot z)
|
14,451
|
\left(1 + x \cdot 2\right) \cdot (1 - x) = -x \cdot x \cdot 2 + 1 + x
|
23,397
|
\sin{k} = z\Longrightarrow \sin^2{k} = z^2
|
33,396
|
B*\vartheta = B*\vartheta
|
3,654
|
(a\cdot c) \cdot (a\cdot c) = c^2\cdot a^2
|
28,184
|
(\dfrac14)^4 \cdot 3/4 = 3/1024
|
-4,360
|
\frac{1}{t^4}\cdot t\cdot \dfrac{1}{48}\cdot 66 = \frac{66\cdot t}{48\cdot t^4}
|
13,128
|
\left(-1\right) + z^2 = (z + 1)*(\left(-1\right) + z)
|
-21,090
|
10/10\cdot \dfrac{3}{10} = 30/100
|
-6,344
|
\dfrac{1}{2 \cdot (x + 6) \cdot \left(8 + x\right)} \cdot 4 = \dfrac{2}{(6 + x) \cdot (x + 8)} \cdot \frac{2}{2}
|
19,810
|
m + 1 + a = 1 + a + m
|
6,234
|
\left((\dfrac{2}{n} + 1)^n\right)^3 = (2/n + 1)^{n\times 3}
|
36,142
|
u^2 + 3*v^2 = (-v - u)^2 + 2*v*(-u - v) + \left(2*v\right) * \left(2*v\right)
|
20,627
|
0 = x^4 - x * x*6 + 1 - 7.2^z\Longrightarrow x^2 = (6 \pm \sqrt{32 - 28.2^z})/2
|
-10,389
|
\frac{1}{240 \cdot (-1) + 60 \cdot s} \cdot 100 = \frac{5}{3 \cdot s + 12 \cdot (-1)} \cdot \dfrac{20}{20}
|
-10,560
|
-\frac{1}{60 (-1) + 15 z}30 = -\frac{10}{20 (-1) + 5z} \frac{1}{3}3
|
51,042
|
4\times 6\times 3 = 72
|
-20,535
|
\frac{9 + x}{x + 9}*\left(-\frac{9}{10}\right) = \frac{1}{90 + 10*x}*(81*(-1) - x*9)
|
1,199
|
x + 2 = 1 + 2 + 3 + \dotsm + x
|
10,224
|
(i + a)\times (j + b) = i\times j + i\times b + a\times j + b\times a
|
12,266
|
\frac{1}{2} \cdot (1 + \cos(2 \cdot p)) = \cos^2(p)
|
36,868
|
\frac{d}{dz} e^{e^z} = e^{e^z}\cdot e^z = e^{e^z + z}
|
-10,765
|
8 = -2 + 5a - 4 = 5a - 6
|
11,208
|
-1 = (\cos(\pi) + \sin(\pi)\cdot i)
|
-639
|
\left(e^{\frac76 \cdot π \cdot i}\right)^5 = e^{5 \cdot 7 \cdot i \cdot π/6}
|
-1,064
|
\frac{1/4\cdot 3}{\frac{1}{8}} = \dfrac{8}{1}\cdot \dfrac14\cdot 3
|
5,149
|
\frac{1}{z x} (x - z) = \dfrac{1}{z} - 1/x
|
27,348
|
\frac{1}{5!} = \frac{1}{120}
|
2,165
|
\frac{1}{S\cdot T} = 1/(T\cdot S)
|
-20,472
|
6/6\cdot \frac{1}{r\cdot 10}\cdot (r\cdot 9 + 9\cdot (-1)) = (r\cdot 54 + 54\cdot \left(-1\right))/\left(60\cdot r\right)
|
-4,998
|
39.5*10 * 10 = 39.5*10^{5 - 3}
|
33,749
|
\pi*10^2 = \pi*100
|
118
|
((-1) \cdot x)/3 = -\frac13 \cdot \frac{1}{3} \cdot x = -x/3
|
21,047
|
3/8 = -\frac18 \cdot 5 + 1
|
6,260
|
b \cdot d^k/b \cdot c \cdot \frac{d^x}{c} = d^x/c \cdot c \cdot b \cdot \frac{d^k}{b}
|
30,334
|
\sin{\varphi} = \cos(-\varphi + \pi/2)
|
-18,960
|
\frac19\cdot 2 = \frac{H_p}{81\cdot \pi}\cdot 81\cdot \pi = H_p
|
27,274
|
g \eta x = g \eta x
|
24,418
|
\tan(x)/\sec(x) = \dfrac{\sin\left(x\right)}{\frac{1}{\cos(x)}}1/\cos(x) = \sin(x)
|
3,982
|
x^2 - x \cdot z + z^2 = -3 \cdot z \cdot x + (z + x)^2
|
12,006
|
1*2*3*\dots*\left(2*(-1) + k\right)*((-1) + k)*k = k!
|
28,808
|
3*(-y + 2*z) = 6*z - y*3
|
3,949
|
\frac{1}{\left(z^2 + 1\right)^{1/2} - z} = (z^2 + 1)^{1/2} + z
|
30,387
|
301 = 350 + 49\cdot (-1)
|
14,261
|
f \cdot u + u \cdot x = u \cdot (x + f)
|
-6,993
|
\frac{4}{5} \cdot 2/3 = \frac{8}{15}
|
-27,688
|
4*\sin(x) = d/dx \left(-4*\cos(x)\right)
|
7,338
|
9\cdot r^2 = x^2\cdot 3\Longrightarrow x \cdot x = 3\cdot r^2
|
5,598
|
1278 (-1) + 8721 = 7443
|
-29,325
|
-3\cdot i - 1 + 10\cdot (-1) = -3\cdot i - 11
|
-9,189
|
60 - x*24 = -2*2*2*3*x + 2*2*3*5
|
10,120
|
3^{H/2} = 2^H + (-1) = 4^{\frac{H}{2}} + (-1)
|
12,494
|
2*x = 135 + 25 = 160 rightarrow 80 = x
|
36,297
|
\cos^2{r} - \sin^2{r} = \cos{r \cdot 2}
|
18,766
|
\left(a - b\right) \cdot \left(a^2 + b \cdot a + b^2\right) = -b \cdot b \cdot b + a^3
|
21,854
|
c \cdot c + a \cdot a + x^2 = \sqrt{a^2 + x^2 + c^2} \cdot \sqrt{a^2 + x^2 + c^2}
|
-20,891
|
\tfrac{l \cdot 72 + 63}{28 \cdot (-1) - l \cdot 32} = -9/4 \cdot \frac{-l \cdot 8 + 7 \cdot (-1)}{-8 \cdot l + 7 \cdot (-1)}
|
-7,672
|
\frac{19 \cdot i + 8}{4 - 3 \cdot i} = \tfrac{1}{4 + i \cdot 3} \cdot (i \cdot 3 + 4) \cdot \frac{1}{4 - i \cdot 3} \cdot (8 + 19 \cdot i)
|
21,230
|
(z*3 + y + 5) (2z + y + 3(-1)) = 15 (-1) + 6z * z + 5zy + y * y + z + y*2
|
16,657
|
\left(x - 35.7 = 4.1\cdot \left(-1.34\right) \Rightarrow x = 4.1\cdot (-1.34) + 35.7\right) \Rightarrow x = 30.206
|
-11,767
|
36/49 = \left(\frac{6}{7}\right)^2
|
11,165
|
(2 \cdot x + 3) \cdot x \leq 2 \Rightarrow 2 \cdot (-1) + 2 \cdot x^2 + 3 \cdot x \leq 0
|
929
|
x * x + b*x rightarrow \left(x + b/2\right)^2 - \left(b/2\right)^2
|
11,296
|
w^2 + 3 x^2 = (x - w)^2 + (x + w)^2 + (x - w) (x + w)
|
31,137
|
1 - \frac{1}{216}*125 = \dfrac{91}{216}
|
22,192
|
1/(b\cdot d) = \frac{1}{d\cdot b}
|
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