id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-6,258 |
\frac{1}{r\cdot 3 + 21\cdot \left(-1\right)} = \frac{1}{(r + 7\cdot \left(-1\right))\cdot 3}
|
15,590 |
\frac{1}{18}\times 10 = 5/9
|
37,057 |
5 = 5 + 0 \times \left(-1\right) = 6 + (-1) = 7 + 2 \times \left(-1\right) = 8 + 3 \times (-1) = ...
|
13,202 |
(\left(-1\right) x)/(-2) = \left((-1) (-x)\right)/\left((-1) (-2)\right) = \dfrac12x
|
15,053 |
\frac{a^h}{a^c} = a^{h - c}
|
11,944 |
y^3*2 + y^2 + 2 y + 5 \left(-1\right) = (y + (-1)) (2 y^2 + y*3 + 5)
|
-20,698 |
\dfrac{h + (-1)}{h\cdot 9 + 9\cdot (-1)} = \frac{1}{9}\cdot 1
|
-26,202 |
14/2 + 3\cdot (-1) + \dfrac13\cdot 6 = 7 + 3\cdot (-1) + 2 = 6
|
26,079 |
1/2 + e^2/2 = \dfrac{1}{2}*(e^2 + 1)
|
14,046 |
-2*z = 1 - z - 1 + z
|
30,645 |
x \cdot x + (7\cdot x + 3\cdot (-1))^2 = 50\cdot x \cdot x - 42\cdot x + 9 = 1 \Rightarrow x^2\cdot 25 - 21\cdot x + 4 = 0
|
7,079 |
0 = 2*\sin^2{y} - 5*\cos{y} + 4*(-1) \Rightarrow \cos^2{y}*2 + 5*\cos{y} + 2 = 0
|
-19,588 |
\frac{1}{\frac{1}{5}}5 / 4 = \frac51 \cdot 5/4
|
30,919 |
(z/2 + z)/2 = z \cdot \frac34
|
-18,591 |
5 \times b + 9 \times (-1) = 10 \times (5 \times b + 5 \times (-1)) = 50 \times b + 50 \times (-1)
|
-12,907 |
4/9 = 8/18
|
19,297 |
(-2) \cdot (-2) + 1^2 - (-2) = 7 = 3\cdot 2 + 1
|
27,558 |
120 - 40 + 30 + 10 \Rightarrow 60 = 50 + 10
|
36,646 |
(12 + 3)^m = 15^m
|
5,275 |
j^4 + j^2 + 1 = (j^2 + 1)^2 - j^2 = (j^2 + j + 1) (j \cdot j - j + 1)
|
30,889 |
(r \cdot e^{i \cdot \theta})^i = r \cdot e^{i^2 \cdot \theta} = r \cdot e^{-\theta}
|
5,269 |
V + U = m - n + U + V rightarrow U + V + m = U + V + n
|
-12,035 |
\frac{31}{45} = \frac{1}{18\cdot \pi}\cdot s\cdot 18\cdot \pi = s
|
-30,539 |
\frac{\mathrm{d}y}{\mathrm{d}x} = 2\tfrac{x}{y^2} = \tfrac{2x}{y^2}
|
7,941 |
H \cdot \left( i \cdot u, x\right) = H \cdot ( -u, i \cdot x) = -H \cdot ( u, i \cdot x)
|
9,557 |
c_1 = (2/9)^{1 + \left(-1\right)}\cdot c_1
|
10,638 |
\frac{3}{3 + 2}\cdot \frac{1}{2 + 2}\cdot 2 = \frac{3}{10} = 0.3
|
-7,052 |
\frac{1}{5 \cdot 2} = 10^{-1}
|
9,896 |
-a + a \cdot f \cdot a = \frac{1}{\frac{1}{a - \frac{1}{f}} - 1/a}
|
-3,423 |
\sqrt{10}*6 = \sqrt{10}*(\left(-1\right) + 5 + 2)
|
-20,020 |
\frac22 \cdot 2/7 = 4/14
|
32,509 |
\rho + z = \rho + z
|
25,527 |
\tfrac{z\cdot 2}{z + (-1)} = 2 + \dfrac{1}{z + (-1)}2
|
9,181 |
(5 + 4 + 3 + 2 + 1)/36 = \frac{15}{36} = \dfrac{5}{12}
|
-5,687 |
\frac{3}{2 \cdot m + 2 \cdot \left(-1\right)} = \frac{1}{(m + (-1)) \cdot 2} \cdot 3
|
37,230 |
1 = b - b*2 \implies b = -1
|
36,609 |
z y + z + y + 1 = 20 = (z + 1) (y + 1)
|
34,697 |
n/2 \leq m\Longrightarrow n/2 \geq n - m
|
37,554 |
\dfrac23 = \dfrac23
|
36,397 |
3 \cdot 3 \cdot 3\cdot 2 \cdot 2\cdot 5 = 540
|
34,055 |
125^2\cdot 5-125^2\cdot 4-24\cdot 125-36=125^2-24\cdot125-36=125\cdot(125-24)-36
|
-1,330 |
\frac{56}{12} = 56\times 1/4/(12\times \dfrac14) = \frac{14}{3}
|
5,243 |
\cot(\frac{1}{4}((-1) \pi)) = \cot(\pi*3/4)
|
-28,934 |
\frac{11}{2}\cdot6=\frac{66}{2}=33
|
19,302 |
(y + m) \cdot (y + m) - \left(m - y\right)^2 = y\cdot m\cdot 4
|
15,764 |
A^6 = A^3 \cdot A^3
|
4,714 |
( a, a*2, \dots) = a
|
-1,248 |
\tfrac{(-4) \cdot 1/3}{6 \cdot \frac15} = 5/6 \cdot (-\frac43)
|
18,799 |
(-m) \cdot (-m) = m \cdot m
|
4,860 |
(120 + 20)\cdot (p + 3\cdot (-1)) = 140\cdot (p + 3\cdot \left(-1\right)) = 140\cdot p + 420\cdot \left(-1\right)
|
12,877 |
(a + b)^2 = (a + b) (a + b) = a^2 + ab + ba + b^2 = a^2 + 2ab + b^2
|
24,693 |
1/(49! \dfrac{1}{43!*6!}) = 1/13983816
|
2,502 |
2^{l + (-1)} + (-1) - |y| + 2^{l + (-1)} = -|y| + 2^l + (-1)
|
26,448 |
4\cdot (-1) + k^4 = (2\cdot (-1) + k^2)\cdot (2 + k^2)
|
-15,133 |
\frac{\nu^4 \cdot p^4}{\frac{1}{\nu^6} \cdot p^8} = \frac{\nu^4}{\frac{1}{\nu^6}} \cdot \frac{p^4}{p^8} = \frac{1}{p^4} \cdot \nu^{4 - -6} = \dfrac{\nu^{10}}{p^4}
|
11,534 |
x^a - y^a = \left(x - y\right) (x^{a + (-1)} + y x^{a + 2 (-1)} + \dots + y^{2 (-1) + a} x + y^{a + (-1)})
|
20,478 |
(z^2 - z + 1)*(z^2 + z + 1) = 1 + z^4 + z^2
|
15,338 |
x * x + 3*\left(-1\right) + 2*x + 4 = 1 + x^2 + 2*x
|
8,286 |
c*x/c = x*\frac{c}{c}
|
5,308 |
2*(-1) + \frac{1}{1 - 2*z}*(1 - 4*z^2) = 2*z + (-1)
|
17,272 |
(-4 \cdot i - 2)/2 = -1 - i \cdot 2
|
-20,956 |
-10/9 \times \tfrac{x + 2 \times (-1)}{x + 2 \times (-1)} = \frac{1}{18 \times (-1) + x \times 9} \times (20 - 10 \times x)
|
52,945 |
6+7=13
|
36,952 |
\binom{x + x - k + (-1)}{x} = \binom{x*2 - k + (-1)}{x}
|
10,766 |
6^k = 2^k\cdot 3^k
|
19,657 |
\left\{3, 1, 4, \dots, 2, 0\right\} = \mathbb{N}
|
16,577 |
\left(x^2 + 4\cdot (-1) = z \Rightarrow z + 4 = x \cdot x\right) \Rightarrow (x \cdot x)^{1 / 2} = \left(z + 4\right)^{\frac{1}{2}}
|
6,767 |
-f g = -fg
|
-3,056 |
175^{1 / 2} - 28^{1 / 2} = -(4*7)^{\frac{1}{2}} + (25*7)^{\frac{1}{2}}
|
-5,456 |
\frac{1}{10 + m \times 2} \times 2 = \frac{1}{2 \times (m + 5)} \times 2
|
-4,659 |
\frac{6(-1) - x \cdot 6}{x^2 + x + 2(-1)} = -\tfrac{4}{(-1) + x} - \frac{2}{2 + x}
|
25,288 |
\sqrt{3} = \sqrt{7 \times \left(-1\right) + 10}
|
27,629 |
1 = -4\cdot 6 + 25
|
38,496 |
m = 1 + m + (-1) + 5\cdot \left(m + \left(-1\right)\right) = 6\cdot m + 5\cdot (-1)
|
40,157 |
\frac{(k + 1)^k}{k^{k + (-1)}} = k \cdot \frac{1}{k^k} \cdot (k + 1)^k = k \cdot (1 + \frac1k \cdot (k + 1) + (-1))^k = k \cdot (1 + \frac1k)^k
|
23,016 |
-(-b*\sqrt{5} + a) = \sqrt{5}*b - a
|
14,716 |
s^{p*u} = \dfrac{s*p*u}{p*u} = \frac1p*s*p*u/u = \dfrac{s^p}{u}*u = (s^p)^u
|
-521 |
\left(e^{\frac{1}{4} \cdot i \cdot 5 \cdot \pi}\right)^2 \cdot e^{5 \cdot i \cdot \pi/4} = e^{\tfrac{1}{4} \cdot \pi \cdot 5 \cdot i \cdot 3}
|
10,399 |
f \cdot D^l = D^0 \cdot D^l \cdot f
|
3,609 |
-4/5\cdot \frac{3}{4} + 1 = 2/5
|
14,777 |
\cos{k y} + i \sin{k y} = e^{i k y} = (\cos{y} + i \sin{y})^k
|
641 |
250 = 10 + h + h*2 + 3*h \Rightarrow 40 = h
|
30,519 |
\tfrac{1}{y^{1 - a}} = y^{(-1) + a}
|
-26,576 |
2\cdot x^2 + 162\cdot (-1) = 2\cdot (x^2 + 81\cdot \left(-1\right)) = 2\cdot (x + 9)\cdot (x + 9\cdot (-1))
|
-7,263 |
\tfrac{12}{91} = 4/13\cdot \frac{6}{14}
|
11,655 |
-g\cdot a_1\cdot a_2\cdot 3 + g^3 + a_1^3 + a_2^3 = \left(a_2 + g + a_1\right)\cdot (g^2 + a_1^2 + a_2^2 - g\cdot a_1 - a_2\cdot a_1 - g\cdot a_2)
|
36,339 |
\cos^2\left(\operatorname{asin}(x)\right) = 1 - \sin^2\left(\operatorname{asin}\left(x\right)\right) = 1 - x^2
|
7,235 |
\frac{1}{4 + 5} 5 = \dfrac{5}{9}
|
11,728 |
\int \sin^4{z}\,\mathrm{d}z = \int (\sin^2{z})^2\,\mathrm{d}z = \dfrac{1}{4}\cdot \int (1 - \cos{2\cdot z})^2\,\mathrm{d}z
|
6,608 |
2 + 4 + 6 + ... + 2 \cdot k = k \cdot \left(2 \cdot k + 2\right)/2 = k^2 + k
|
14,419 |
1 + 2\cdot (l^2\cdot 2 - l\cdot 6 + 2) = 4\cdot l^2 - 12\cdot l + 4 + 1
|
16,553 |
k + (-1) + k = 2 \cdot k + (-1)
|
7,611 |
(2 \cdot 13)^4 + (120^2 + 119^2) \cdot (-119^2 + 120 \cdot 120) + 13^4 = \left(2 \cdot 2 \cdot 13\right)^4
|
24,348 |
|B| = |-B|
|
30,393 |
\frac{15\times 14}{2\times 3} = 35
|
2,298 |
y_i^5 = -y_i^2 \cdot y_i - m \cdot y_i^2 = y_i + m - m \cdot y_i^2
|
9,354 |
f \cdot d = \frac14 \cdot \left(-(f - d) \cdot (f - d) + \left(f + d\right)^2\right)
|
22,008 |
\mathbb{E}(V_2 + V_1) = \mathbb{E}(V_2) + \mathbb{E}(V_1)
|
2,947 |
(g_l + g_l + g_l + g_l + g_l) \cdot (g_i + g_i) = 2 \cdot g_i \cdot 5 \cdot g_l
|
9,449 |
x + g - \theta = -(\theta - x) + g
|
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